To add to the above. You have to buy out the 50% value at the current market price (unless some preferential terms apply to you, in which case they would be in your current agreement). The house will have to be valued, and you agree with the valuation. Then you would need a additional mortgage for 50% of this figure, which you start repaying back to the mortgage company each month. You obviously cease to pay to the HA the 'rent' on the 50% share they currently own. I'm sure you appreciate that the reduction in rent paid will be less than the increase paid to the mortgage company. But you will own the house.