I was in this position 2 years ago. Me and my ex bought a house in joint names, had a baby together and 9 months down the line he left, just walked out. I carried on paying the mortgage, life insurances (in joint names), every month with a struggle, after 16 months I decided to sell up as me and my new partner were buying our own property together. I had to have my exs permission to sell the property which he agreed to straight away, (this was all through the solicitors). He was entitled to half of the equity, but I fought tooth and nail to get back what I had paid. I had to prove that I had made the payments each month which I did from my bank account which was in my own name as when he left I cancelled the joint account straight away. Lucky for me my ex agreed that I have back the mortgage payments and insurances out of the equity before the remainder was split 50/50. But by law the equity from the sale of the house should be split 50/50.