Sadly, as she is shown to be an equal owner she is entitled to a 50% share of the equity regardless of 'who paid what' unless you have written agreement to the contrary or own the property as tenants in common with differing shares, rather than joint tenants.
Equally, she is just as liable for any debts as you are.
She will say you have had the benefit of living in the property since she left and haven't paid her any rent to her for the privilege of having sole occupancy.