To whom does the house belong?
When a couple divorces, assets (including the marital residence) are divided in accordance with state laws. Property division rules can vary considerably from state to state, so check your state's laws (or check with an attorney) to see which rules your state enforces.
Community property states
Community property states focus on the difference between separate property (that which you bring to the marriage, inherit during the marriage, and receive as a gift during the marriage) and community property (that which is acquired during the marriage). Separate property can usually be kept by the owner-spouse after a divorce, while community property is usually divided equally between the spouses.
Equitable distribution states
The majority of states are equitable distribution states. These states generally agree that the couple's property is marital property and should be divided between the spouses equitably and fairly. Some of these states will make exceptions for separate property, such as inheritances and gifts, and some will not.