Is my partners ex entitled to half the house?

My partner paid a deposit left by her late father 3 years ago and moved in with her ex they were not married but have a child together. One year after moving in the split up. He made half the payments for the mortgage in those 12 months and no more since. Although he paid nothing towards the house he wants half of the value. If we sell will he get half of the equity to take his name off the mortgage or only the amount he has paid? He is very awkward and quite honestly a pain. We are hoping to move but this is stopping us aas we don't know what he is legally allowed and can't afford a solicitor

Please help

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