You are thinking that this happens in sequential steps. It does not, it happens all at once.
Eg.
You have a pension worth $200k
He has a pension worth $100k
Together you have a house worth $400k (value of house minus mortgage)
If he keeps the house, then his net worth is 500k, and yours is 200k, so he owes you $150k.
If you keep the house, then his net worth is 100k, and yours is 600k, so you owe him $250k.
If he cannot come up with $150k to pay you, then he cannot keep the house. If you cannot come up with $250k to pay him, then you cannot keep the house.
Assuming that neither of you can come up with the appropriate payment, then the house is sold.
In the event that the house is entirely in his name, or you sign it over to him, you are probably still roughly fine. He still owes you the $150k, and he has a large fixed asset. There are legal steps to ensure that he cannot sell the house without paying you first. That said, easier to make sure that your ex does not get title to the house until equalization is decided.