New Hampshire

Can a known donor renounce his legal obligations as a parent?

Yes; a sperm donor will not be held liable for child support if he has signed an agreement to that effect with the party / parties receiving the sperm.

What if a known donor attempts to enforce his parental rights when the original intent was to be a sperm donor only?

Unknown, but this may be possible given the lack of statute or case law cutting off the rights of a sperm donor.

Does the state allow for second-parent adoption (i.e., for same-sex couples)?

Some courts have permitted second-parent adoptions.  Given that the state recognizes same-sex marriage, married same-sex couples can jointly adopt or do a second-parent adoption.

Does the state allow for multiple-parent families (when the child has more than two adults in a parenting role)?

Unknown; this issue has not yet been addressed.

Does the state recognize “de-facto” or “psychological” parentage (of an “acting” parent without a biological connection) or a similar concept?

Unknown; this issue has not yet been addressed.