Is it true that if a biological father signs over rights to the children to the mom, that he no longer is responsible for child support? Does it vary by state? This is in NY.

No its not true unless an adoption were to take place and there is someone waiting in the wings to accept full responsibility.

Well first the father can not just sign over custody, he has to go to court. And it is very hard to lose your rights and almost impossible to give them up.

In almost all cases except for adoption of the child, the father will still have to pay child support if somehow he could give up his rights.

No, it's not true in NY - you can't sign off your rights unless someone is willing to adopt and support the child.

I'm just parroting what has already been said but I am in NY.