An Assumption Agreement is a legal document through which one party transfers its obligations or duties under a contract to another party. A person who assumes a mortgage takes over a payment from the previous homeowner.It allows one party to "assume" the rights and responsibilities of the other party. An assumption agreement is a kind of legal document that you'll find commonly used in finance and real estate transactions. An assignment and assumption agreement is a contract that allows one of the parties to transfer their contractual rights and duties to another party. Mortgage assumption allows a buyer to take on the original loan balance at the original terms, but it doesn't account for any home equity the seller has built. A mortgage assumption agreement is basically you coming in and saying sign this paperwork I'm still responsible for the mortgage. Assignment and Assumption.