<?xml version="1.0" encoding="US-ASCII"?>
<!--XBRL Document Created with Wdesk from Workiva-->
<!-- -->
<link:linkbase xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <link:roleRef roleURI="http://prth.com/role/Cover" xlink:href="prth-20200617.xsd#Cover" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedNetLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodEndLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodStartLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTerseLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel" xlink:type="simple" />
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/netLabel" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel" xlink:type="simple" />
  <link:presentationLink xlink:role="http://prth.com/role/Cover" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CoverAbstract" xlink:label="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:type="locator" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_DocumentType" xlink:label="loc_dei_DocumentType_92065889C72A51D8B0FECB046880D5E9" xlink:type="locator" />
    <link:presentationArc order="1" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_DocumentType_92065889C72A51D8B0FECB046880D5E9" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_DocumentPeriodEndDate" xlink:label="loc_dei_DocumentPeriodEndDate_1E3A655C748553D2A034E6B5AFCAFD23" xlink:type="locator" />
    <link:presentationArc order="2" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_DocumentPeriodEndDate_1E3A655C748553D2A034E6B5AFCAFD23" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityRegistrantName" xlink:label="loc_dei_EntityRegistrantName_EBC8123D2BFC58DC8BA14523A0E7D8B5" xlink:type="locator" />
    <link:presentationArc order="3" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityRegistrantName_EBC8123D2BFC58DC8BA14523A0E7D8B5" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityIncorporationStateCountryCode" xlink:label="loc_dei_EntityIncorporationStateCountryCode_7BDF94F393315B5A92B86E3424800544" xlink:type="locator" />
    <link:presentationArc order="4" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityIncorporationStateCountryCode_7BDF94F393315B5A92B86E3424800544" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityFileNumber" xlink:label="loc_dei_EntityFileNumber_E478DB69927F5ACCB7890FAC54D57C8F" xlink:type="locator" />
    <link:presentationArc order="5" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityFileNumber_E478DB69927F5ACCB7890FAC54D57C8F" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityTaxIdentificationNumber" xlink:label="loc_dei_EntityTaxIdentificationNumber_262D55EF8385517CA4E5F1C8E0558602" xlink:type="locator" />
    <link:presentationArc order="6" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityTaxIdentificationNumber_262D55EF8385517CA4E5F1C8E0558602" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressAddressLine1" xlink:label="loc_dei_EntityAddressAddressLine1_39FD34F8A9E85593A9C938EA8E889D27" xlink:type="locator" />
    <link:presentationArc order="7" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityAddressAddressLine1_39FD34F8A9E85593A9C938EA8E889D27" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressAddressLine2" xlink:label="loc_dei_EntityAddressAddressLine2_34A3F7E2D4515F3F9D062051A494883E" xlink:type="locator" />
    <link:presentationArc order="8" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityAddressAddressLine2_34A3F7E2D4515F3F9D062051A494883E" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressCityOrTown" xlink:label="loc_dei_EntityAddressCityOrTown_D819231B36615FCB8766310AFA10C776" xlink:type="locator" />
    <link:presentationArc order="9" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityAddressCityOrTown_D819231B36615FCB8766310AFA10C776" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressStateOrProvince" xlink:label="loc_dei_EntityAddressStateOrProvince_4FB954D2669B567B91EBCE1909F5D517" xlink:type="locator" />
    <link:presentationArc order="10" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityAddressStateOrProvince_4FB954D2669B567B91EBCE1909F5D517" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressPostalZipCode" xlink:label="loc_dei_EntityAddressPostalZipCode_147ACD2585575B6C835E16D6BAD324B7" xlink:type="locator" />
    <link:presentationArc order="11" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityAddressPostalZipCode_147ACD2585575B6C835E16D6BAD324B7" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CityAreaCode" xlink:label="loc_dei_CityAreaCode_DDA66393567550038D3D163D9F4CD179" xlink:type="locator" />
    <link:presentationArc order="12" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_CityAreaCode_DDA66393567550038D3D163D9F4CD179" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_LocalPhoneNumber" xlink:label="loc_dei_LocalPhoneNumber_A882874B644D55F280B1E4F857AD8D61" xlink:type="locator" />
    <link:presentationArc order="13" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_LocalPhoneNumber_A882874B644D55F280B1E4F857AD8D61" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_WrittenCommunications" xlink:label="loc_dei_WrittenCommunications_B350538305205DCDA967D4C0DCF57ABE" xlink:type="locator" />
    <link:presentationArc order="14" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_WrittenCommunications_B350538305205DCDA967D4C0DCF57ABE" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_SolicitingMaterial" xlink:label="loc_dei_SolicitingMaterial_E33B11BE210657CC827962BDD8ECE15D" xlink:type="locator" />
    <link:presentationArc order="15" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_SolicitingMaterial_E33B11BE210657CC827962BDD8ECE15D" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_PreCommencementTenderOffer" xlink:label="loc_dei_PreCommencementTenderOffer_D0B5CA7D28E55B839C242B5E456F5295" xlink:type="locator" />
    <link:presentationArc order="16" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_PreCommencementTenderOffer_D0B5CA7D28E55B839C242B5E456F5295" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_PreCommencementIssuerTenderOffer" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_179BFD8237BC5348B6F76F3281EFED0B" xlink:type="locator" />
    <link:presentationArc order="17" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_179BFD8237BC5348B6F76F3281EFED0B" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_Security12bTitle" xlink:label="loc_dei_Security12bTitle_58A2AA858A8D5A408F4D38939B302B06" xlink:type="locator" />
    <link:presentationArc order="18" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_Security12bTitle_58A2AA858A8D5A408F4D38939B302B06" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_TradingSymbol" xlink:label="loc_dei_TradingSymbol_DD9CD2C1055F5EA8811E128DC525B932" xlink:type="locator" />
    <link:presentationArc order="19" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_TradingSymbol_DD9CD2C1055F5EA8811E128DC525B932" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_SecurityExchangeName" xlink:label="loc_dei_SecurityExchangeName_67DB65D3B4BA59D3B9874C152ED90E75" xlink:type="locator" />
    <link:presentationArc order="20" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_SecurityExchangeName_67DB65D3B4BA59D3B9874C152ED90E75" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityEmergingGrowthCompany" xlink:label="loc_dei_EntityEmergingGrowthCompany_00897091FFA154BE90775906635FBBB5" xlink:type="locator" />
    <link:presentationArc order="21" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityEmergingGrowthCompany_00897091FFA154BE90775906635FBBB5" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityExTransitionPeriod" xlink:label="loc_dei_EntityExTransitionPeriod_743C722EBF7E5FD9A203176B982F1D6E" xlink:type="locator" />
    <link:presentationArc order="22" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityExTransitionPeriod_743C722EBF7E5FD9A203176B982F1D6E" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityCentralIndexKey" xlink:label="loc_dei_EntityCentralIndexKey_C63B7C907FB55BC1A9AD8CDC627B4082" xlink:type="locator" />
    <link:presentationArc order="23" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_EntityCentralIndexKey_C63B7C907FB55BC1A9AD8CDC627B4082" xlink:type="arc" />
    <link:loc xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_AmendmentFlag" xlink:label="loc_dei_AmendmentFlag_E2F153A24E9F58CAA185C228C4BA4B9D" xlink:type="locator" />
    <link:presentationArc order="24" preferredLabel="http://www.xbrl.org/2003/role/terseLabel" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_2E86585CE5455326AE82EEA0344BF063" xlink:to="loc_dei_AmendmentFlag_E2F153A24E9F58CAA185C228C4BA4B9D" xlink:type="arc" />
  </link:presentationLink>
</link:linkbase>
