This type of agreement transfers the obligations of one party under a contract to another party. It allows one party to "assume" the rights and responsibilities of the other party.(h) Capitalized terms used and not otherwise defined in this Exhibit 4.13 shall have the meanings assigned to such terms in the Agreement. A mortgage assumption agreement is basically you coming in and saying sign this paperwork I'm still responsible for the mortgage. Loan assumption is when you take over full responsibility of the mortgage loan.