Two equal or co-owners are, as a general matter, entitled  to half the equity, so if you and your fiance are both on the title, you are each entitled to half. That said, a court--such as in a partition suit--would typically adjust for each person's relative contribution in order to be fair or equitable. Say the house is now worth $500k, but was purchased for $400k; one person paid a total of $150k, while the other paid a total of $250k. The court might give that second person, who paid $100k more, the first $100k of equity and then split the remaining $400k of equity 50-50. There are other ways a court might do it, but the principal is, the court would try to be fair and reflect that one person paid significantly more. It would be good to bear that in mind when trying to work out a fair price, since if it goes to litigation, there wlll often--not always but often--be some adjustment if this matter goes to court.