My ex-husband has asked to relinquish his parental rights. I have had the children with me since last May (2008). The relationship he has with my daughters has disintegrated to almost nothing. I am capable of supplying their needs. I need to know what the laws are regarding this. I need a form to file with the court. I would really like to have full rights to the children. He doesn't help with doctor visits, school engagements, etc. I want to make sure they are always covered by insurance, and if an emergency happens, I don't want to have to wait for him. He has clearly stated that he wants nothing to do with me, and our relationship has become untenable.

There are hundreds of threads in this forum plus a sticky note that answers your question.

Bottomline is courts are very reluctant to grant a TPR. Generally they will only be granted to clear the way for an adoption or if the parent represents a danger to the child.

But you don't really want a TPR. What you want is sole legal and physical custody. You should be able to get that. Just go back to court and ask for a modification of the custody agreement. If he wants nothing to do with the kids, then he may not show up to protest and it will be granted by default.

In an emergancy why do you have to "wait" on hm, sounds like you truly have a misunderstanding or you have a lousely child custody agreement.

He can not just give up his rights, he does not have to use them, he can go away and never call or do anything.
You have full rights with your children when they are with you. You never have to wait on him, merely inform him normally.
So you merely file to have your current order modified, giving you sole custody but physically and legally.
Then he does not ask for any visits and it is out of it. He will have to of course still pay child support but that does not stop.
ON health insurance so you get your own, if he is not doing it, you do it anyway without him