Thank you for your question
My name is Clare
I shall do my best to help you but I need some further informtaion first
How much is the house worth now and how much is outstanding on the mortgage?
Why did you agree to the property being placed in joint names?
Do you mean he had to be added to the mortgage in order for you to remain there?
Did he actually bring any capital to the property?
May I ask why you did not have a Declaration of Trust drawn up this time?
Did you discuss it at all?
Would he sign one now?
Your best bet would be to get one signed now as otherwise there is a risk that he could indeed claim 50% of the full equity.
You could certainly argue that you did not mean to give him half of the property - and it is likely that you would succeed - but only after an expensive court battle
Please ask if you need further details