Quoting Kay plus Three:" In NH, a parent cannot sign off their rights unless there is someone else taking over. Meaning he can't ... [snip!] ... for him. The state of NH will not allow just one parent to be fully responsible for a child in case of emergency or death."
I think in Kansas, a parent can sign over their rights, but they're still responsible for child support until the kid is adopted (if ever). A girl I knew a long time had her BD "give up" his rights, but he still paid CS.
That was well over 15 years ago though, the laws could have changed by now.