When I split with DS1's dad, I had just bought my house 8 months earlier.
In my own name.
Made life extremely simple.
He moved out. With nothing. Nothing but his clothes and playstation.
No divorce - not married. No money to divide - no savings. So very simple. I hear of messy divorces and think, thank fuck.
Please get the mortgage on your own. Mine is still in my own name, and will stay this way until I no longer give a crap about having a home for my boys!