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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019f811f-f366-7d68-981d-1d063e650140,g:bdacb1c6-2edb-4196-8cb3-37b6aadaf217-->
<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://rithmcap.com/role/Cover" xlink:type="simple" xlink:href="rhome-20260731.xsd#Cover"/>
  <link:presentationLink xlink:role="http://rithmcap.com/role/Cover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_019f811f-f366-756a-af19-14748e09ba4e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_DocumentType_019f811f-f366-756a-af19-14748e09ba4e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_019f811f-f366-7962-8755-9da3921b74ba" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_DocumentPeriodEndDate_019f811f-f366-7962-8755-9da3921b74ba" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_019f811f-f366-783a-a91c-adcb6ff514a5" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityRegistrantName_019f811f-f366-783a-a91c-adcb6ff514a5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_019f811f-f366-73c1-829d-9df15063d8cb" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityIncorporationStateCountryCode_019f811f-f366-73c1-829d-9df15063d8cb" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_019f811f-f366-701c-9ecc-a37987f7cba5" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityFileNumber_019f811f-f366-701c-9ecc-a37987f7cba5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_019f811f-f366-7983-b563-6ebc05acb35d" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityTaxIdentificationNumber_019f811f-f366-7983-b563-6ebc05acb35d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_019f811f-f366-7b22-b6cd-5704a891883f" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityAddressAddressLine1_019f811f-f366-7b22-b6cd-5704a891883f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_019f811f-f366-733d-96d1-8f7ac79cda80" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityAddressCityOrTown_019f811f-f366-733d-96d1-8f7ac79cda80" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_019f811f-f366-706d-ad3f-6e9d4677678c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityAddressStateOrProvince_019f811f-f366-706d-ad3f-6e9d4677678c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_019f811f-f366-7d6c-a5f6-1b69b848f3ca" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityAddressPostalZipCode_019f811f-f366-7d6c-a5f6-1b69b848f3ca" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_019f811f-f366-796e-88e4-f11a4d37032c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_CityAreaCode_019f811f-f366-796e-88e4-f11a4d37032c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_019f811f-f366-7079-a84f-2a508c1c746c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_LocalPhoneNumber_019f811f-f366-7079-a84f-2a508c1c746c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_019f811f-f366-7a28-9f6d-a2d070215b7c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_WrittenCommunications_019f811f-f366-7a28-9f6d-a2d070215b7c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_019f811f-f366-796f-91c6-b9b55588817a" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_SolicitingMaterial_019f811f-f366-796f-91c6-b9b55588817a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_019f811f-f366-775d-bf05-318d79035fb4" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_PreCommencementTenderOffer_019f811f-f366-775d-bf05-318d79035fb4" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_019f811f-f366-72b2-92dd-2f2db516717b" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_019f811f-f366-72b2-92dd-2f2db516717b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_019f811f-f366-7294-976f-2eccde1c433c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityEmergingGrowthCompany_019f811f-f366-7294-976f-2eccde1c433c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod_019f811f-f366-71df-a309-19912f80c0c0" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityExTransitionPeriod_019f811f-f366-71df-a309-19912f80c0c0" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_019f811f-f366-7d19-b0c4-a16d214ba0f3" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_EntityCentralIndexKey_019f811f-f366-7d19-b0c4-a16d214ba0f3" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_019f811f-f366-7dd4-8021-bc111f83d54f" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019f811f-f366-7e19-a861-0110ff4795c0" xlink:to="loc_dei_AmendmentFlag_019f811f-f366-7dd4-8021-bc111f83d54f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
