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My brother in law and his 'girlfriend' too out a joint mortgage on a property a couple of years ago.
Relationship has turned sour and she announced at the weekend that she was moving out to go stay in another property she owns.
So....I have strongly suggested to him that they really need to go to a solicitor as I can see him not receiving any money and then defaulting on the mortgage payments, etc. Legal agreement for her to continue financial contributions until such time as property sold or whatever.
What else?
Loads of aggro if you're unlucky. One party can just stop paying the mortgage. Or they can chase for their half of the house. Google Kernott vs Jones. Legal fees will very quickly make who is in the right a bit academic.
Best thing to do is get on reasonable terms ASAP and get a settlement agreement drafted and signed.
They need a solicitor each and then draft an agreement on what does/gets what.
It takes less time than buying a house but it still takes a surprising amount of time to conclude.