If a father terminates all parental rights can he terminate, if agreed upon with myself, child support... :mad:

In the state of NH...

And if that in turns can happen does that mean I lose out on a chance for welfare assistance?

When you apply for welfare they automatically have you sign up for child support. So you are doing a vicious circle wasting your time and hurting yourself if you do that.
In my state there are a lot of guys that pay child support and collect welfare for themselves.
Even if he terminates his rights the state will still come after him for child support. There isn't much point in terminating his rights.

It doesn't matter if he terminates his rights or not. He will still be liable for child support. Him terminating his rights won't effect you getting welfare at all.