My 2nd ex owned the house before we got married...I asked for no equity from the improvements (and we are talking major repair stuff from replacing main beams of the house to adding central air/heat, new windows, paving driveway, new wrap around deck & privacy fencing).
I had already moved with the kids when he filed for divorce so he kept the house and refinanced to get my name off the loan.
First ex wouldn't leave me alone so I moved out of the mobile home we had with my daughter and our son and offered to give it to him...when he said he was moving out (a ploy to get me to move back in so he could continue to bother me), I sold it very cheap.