it all depends who paid the mortgage etc etc, if you paid it equally then you will have to buy out the other persons half, but if you can prove that you paid the mortgage and most of the bits and pieces then the court will go in favour of you and you will either get all of it or not have to buy out as much.
At the moment its all cool. Both of us have agreed to sell but the worry is that if we have to wait till the market improves she might be "settled" again and have changed her mind. Got a summet meeting sunday before Guildford with her ,so hopefully sort things then.
It helps if you have documents to prove that you have been the main bill payer and maybe the higher input of deposit.
Me and my ex went through a similar process a year ago. I wanted to buy her out and she wanted to sell it straight-up.
In the end she settled for a good lump sum.
Don't forget that by selling you will be incurring mortgage settlement fees, legal fees etc that will accumulate possibly a few grand pending how long your fixed rate has left (if you have a fixed rate). Add to that the loss of a mortgage when they are so hard to get nowadays.
Obviously I don't know your situation but have a good think about making a settlement demand to them including all things you want to keep or sell from the house. You can negotiate on details like fixtures and fittings.
best of luck and if you need any advice feel free to pm me !