The Moneyist: My abusive ex never contributed to our home’s mortgage. Do I still owe him half the equity if his name is on the deed?

Dear Quentin,

My physically abusive ex and I separated a year ago (we were not married); we have two children together. I have a restraining order against him and I have primary custody of the children. 

Seven years ago, we bought a house. Both of our names are on the title but only my name is on the mortgage, since I was the only one with…