Buying out ex-spouse for home

How does it work when you want to buy out the other party’s share of equity, but there is no equity? In this situation, the home is worth less than is owed. Who owes whom what?

It depends on the agreement of the parties, negative equity can be split (the outspouse pays the inspouse) or the home is simply transferred to the inspouse without money changing hands.

How can you transfer the deed of trust to the inspouse, getting off of both the deed of trust and the title, when the inspouse is the dependent spouse?

The loan must be refinanced.