One question I get asked a lot is what paperwork is needed in New Hampshire so that a husband/boyfriend can agree to give up his rights to a child that hasn’t yet been born (or, sometimes, even conceived).
The short answer is that there’s no such paperwork. Public policy prohibits a man from simply agreeing that he shall not have any parental responsibilities for his own child. The child’s interests in having financial and other support from both parents is considered paramount.
The longer answer is that there are limited situations in which a man can be a sperm donor, and thus have no rights or responsibilities of parenthood. Often, this happens via an anonymous donation using a sperm bank.
However, sperm donation can also happen with a known donor, with one major caveat: this is very dangerous legal territory and it is essential that both the donor and the intended parent(s) be represented by qualified attorneys through the process. Failure to do things exactly right can lead to the sperm donor being considered the legal father of the resulting child. A quick Google search brings up plenty of news articles with that exact result.
Whether your husband/boyfriend/ex-husband/ex-boyfriend can be your known sperm donor is a very complex legal question and can only be answered by your attorney after a thorough discussion of your personal situation. If you are considering going down this path, it is essential that you speak with an attorney before proceeding. In additional to the complex legal issues, there are complex social issues to consider and a consultation with a mental health professional experienced in third-party reproduction is also important. For most couples (or former couples), participating in such an arrangement is ultimately not advisable.