Infidelity/WAH, my story pt 7

[ForGump]

The best case scenario is that your WH simply does not claim any rights to the house.

More middle of the road scenario is that whatever equity there is in the house (probably just the down payment, since you're just buying it now), you have to find a way to pay off 50% of that to your WH.

Worst case, your WH doesn't want to be bought out, he wants to keep the house; and you have to battle over it.