You can let him have the house, but don't let him not pay you for your share of the equity.

From your post on the other board, he doesn't stand a chance of getting custody with his work schedule. Child support will be what the guidelines say they are.

And the state can garnish it from his wages. If he is in a job where he is considered a consultant and doesn't get paid through the payroll dept, then it won't be garnished and he will have to send the child support check to the agency that collects child support. And if he doesn't pay, it can be a while before anything is done.

Which is why you don't give up your share of the marital asset.

And tie his being current on child support by the end of the year into his getting the tax exemption on your child when it is his year to claim him.