As a half owner (on the deed with you), they are entitled to half the profits from the house: in buying a home with another person and putting them on the deed, you entitled them to a proportionate share of the home's value--you don't put someone on the deed unless you are willing to share the proceeds with them.You write that they did not live in house, pay the mortgage or taxes, etc. The implication is that you did. That means that you already received value for having paid the mortgage and taxes--you had a place to live; therefore, paying those things gives you no claim to a higher share of the proceeds, since you have already been compensated (by having a home to live in) for them. And  living in a property by itself conveys no right to more of the proceeds, and not living in a property does not reduce or impair someone's right to the equity: many real estate owners and investors do not live in the property they own, but nonetheless are entitled to their full share (based on how much of an owner they are) of the value. Residence and ownership do not impact each other.