If the house has gone up in value then your friend will be entitled to receive her half share of the increase in value, but she should expect the notional costs of sale, the estate agents and legal fees that would be incurred if you actually did sell, to be taken of the value first. That is probably the easy bit. The real issue is to transfer the property into your sole name, and to do this you will have to get the mortgagee to agree. They will only do that if they are satisfied that you can afford to repay the mortgage, and a mortgage of three or four times ones income isthe usual maximum. If they do agree they will expect their fees to be paid, and there will be legal fees and Land Registry fees as well. So -1) agree how much, if anything, you will need to pay your friend, -2) Approach your mrtgagee and ask if they will agree to the property, and mortgage being transferred into your sole name, -3) If they will they will charge you fees, and you will need to have a solicitor, or possibly the mortgagees solicitor deal with the paperework.