If he owes you past due support the amount does not go away just because he got the children. The court has a variety of ways to handle the situation if you and he cannot agree. Usually, depending on the amount of the monthly obligation and the needs of the children the court can offset the entire amount until he catches up or some percentage until he catches up-maybe 75% would be deducted from your obligation so you would give him credit that 75% and pay him the other 25%.
Talk to a lawyer to help you negotiate and to draw up final papers.
I agree with both attorneys. Most often what happens is the child support that you would owe him is offset by the arrearages. What the Court would do would be determine what his arrears are, then determine what your child support would be, and basically you don't pay until the amount of arrearages is reached which would be determined by what your support would be on a monthly basis. So your child could potentially reside with the father for months before child support would become due. You should contact an attorney. Good luck.
Sincerely,
B. Elaine Jones, Esq.