<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2020 Workiva-->
<!--r:74e8a08c-a2f4-4456-a0b8-dcb28bb111e7,g:5289be26-1974-4b13-8fbe-18f1624f57dc-->
<link:linkbase 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" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://prth.com/role/Cover" xlink:type="simple" xlink:href="prth-20201210.xsd#Cover"/>
  <link:presentationLink xlink:role="http://prth.com/role/Cover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_01e34b2a-1472-42f5-8b5e-1b0486773f65" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_DocumentType_01e34b2a-1472-42f5-8b5e-1b0486773f65" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_a354376a-6f20-4057-9d0e-fd9a4e070831" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_DocumentPeriodEndDate_a354376a-6f20-4057-9d0e-fd9a4e070831" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_4035f6e0-b081-4094-bfea-ca5261ae06f3" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityRegistrantName_4035f6e0-b081-4094-bfea-ca5261ae06f3" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_68719985-c626-4306-adc1-41d94cd7a898" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityIncorporationStateCountryCode_68719985-c626-4306-adc1-41d94cd7a898" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_5dfefa01-5f72-4b5d-9c8e-c8951179d4a1" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityFileNumber_5dfefa01-5f72-4b5d-9c8e-c8951179d4a1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_f9941706-3769-494e-9a97-4a3317be43b8" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityTaxIdentificationNumber_f9941706-3769-494e-9a97-4a3317be43b8" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_3d4e13a4-406c-47e2-b804-2c7ceb964046" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityAddressAddressLine1_3d4e13a4-406c-47e2-b804-2c7ceb964046" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2_7386a42d-8442-4583-83b4-c29ebb4455bc" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressAddressLine2"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityAddressAddressLine2_7386a42d-8442-4583-83b4-c29ebb4455bc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_3e0d8f58-8c66-4f0b-bb07-883ed21592e1" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityAddressCityOrTown_3e0d8f58-8c66-4f0b-bb07-883ed21592e1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_712e2845-bac6-4d73-a5e1-c70d714ef4a5" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityAddressStateOrProvince_712e2845-bac6-4d73-a5e1-c70d714ef4a5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_4675f09a-7f26-4027-92ff-2edb304f6587" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityAddressPostalZipCode_4675f09a-7f26-4027-92ff-2edb304f6587" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_58496095-5f96-4148-9357-dcfbb568f68c" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_CityAreaCode_58496095-5f96-4148-9357-dcfbb568f68c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_11e6f91b-59ba-4a04-a40c-353c7a54f058" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_LocalPhoneNumber_11e6f91b-59ba-4a04-a40c-353c7a54f058" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_b6b7a4b6-63cb-44f0-b83f-8a60838e5f48" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_WrittenCommunications_b6b7a4b6-63cb-44f0-b83f-8a60838e5f48" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_d8986b06-df16-453d-a44a-3e675abbfdcf" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_SolicitingMaterial_d8986b06-df16-453d-a44a-3e675abbfdcf" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_a0fcb4cc-ca9f-4938-9c53-0cd8a2b11a67" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_PreCommencementTenderOffer_a0fcb4cc-ca9f-4938-9c53-0cd8a2b11a67" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_1f4a9f62-4d56-4295-bf81-18de8f21902d" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_1f4a9f62-4d56-4295-bf81-18de8f21902d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_51cf87e5-22ed-43f5-8717-338578cf4407" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_Security12bTitle_51cf87e5-22ed-43f5-8717-338578cf4407" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_b97d287b-8358-4aa6-8600-ed58e335f054" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_TradingSymbol_b97d287b-8358-4aa6-8600-ed58e335f054" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_6f37572e-38f2-4d0d-aabb-c16b8a965c49" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_SecurityExchangeName_6f37572e-38f2-4d0d-aabb-c16b8a965c49" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_5f038efb-3252-49fe-b7c7-423151e26056" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityEmergingGrowthCompany_5f038efb-3252-49fe-b7c7-423151e26056" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod_8b446734-6c4f-44ad-8da2-496efa37e0d6" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityExTransitionPeriod"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityExTransitionPeriod_8b446734-6c4f-44ad-8da2-496efa37e0d6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_73dedbd3-fa7d-4ecd-a866-e463cac604d5" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_EntityCentralIndexKey_73dedbd3-fa7d-4ecd-a866-e463cac604d5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_0dbd5e3b-6916-4e74-835d-897c57a2e181" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="24" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_0e7a1ec2-d635-4d37-bb28-89aae420ded5" xlink:to="loc_dei_AmendmentFlag_0dbd5e3b-6916-4e74-835d-897c57a2e181" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
