That is up to your husband. If he doesn't mind having his name on a property that he is not entitled to other then financially, then leave it be. But most likely, for his safety; he will want his name off of it due to possible credit problems. Regardless if you got the house in the divorce, if his name is still on the mortgage he is held responsible for the payment...that puts a lot of trust in you. I personally would want my name off, because you never know what could happen. Good luck!
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~MySonsMom~