My ex husband wants to sign over rights to my fiance

What does your lawyer advise?

I don't understand what that means.....

Neither do I. He has no financial rights, but it very much sounds like he has some enforceable financial responsibilities. I'm willing to bet he wants to dump the support payments and keep the parental rights.

What won't they think of next.

He doesn't want to pay child support at all. He wants my fiance and I to be fully financially responsible for the children. Honestly, we would love it if he would just sign them over. But I'm not sure a court would let him do that.

You and your finance are not married, so he can't adopt the kids - which is what your dead-beat ex wants so he will be off the hook, financially.

If you are in the US, you will have to go thru the courts anytime the children are concerned.

I would be very surprised to see a court reassign financial responsibility. I doubt anything short of adoption will alter that. Old business saying "You can delegate authority, but you cannot delegate responsibility, and this is what the father seems to be seeking. The court will likely be guided by what it considers to be the best interests of the child.

Not true at all see the case of Brad Pitt and Angelina Jolie adopting three children together as a non-married couple.

Even if your fiancé (who can possibly be a part of the adoption of your child even though you are not yet wed; check the laws in your state) takes on full financial, etc. responsibility, your ex-husband isn't going to be absolved from paying back child support.

Get thee to a lawyer. Get your divorce and child support agreement altered to garnish your ex's wages and possibly even repo some of his possessions in order to pay the old debts. They will not be discharged by an adoption. This is not like declaring bankruptcy.