I'm trying to find out the statute of limitations on child abandonment, when can I file against the father of my child and after a certain period can I terminate his rights even if he said he won't do so voluntarily? She's only 10 months old and he doesn't come to see her or pay child support and doesn't plan on it.

So he doesn't plan on paying child support why allow him to get away with it scott free?

You go apply for child support and don't let him make you feel sorry for him.
He might not pay but that doesn't mean you shouldn't have an order of support against him.
His problem not yours.

It is not as simple as signing away his rights and that still doesn't sign away his responsibility to pay child support.
If you ever go for welfare they will make you go after him for support.