@leslie82 I'm really not interested in getting into an argument about it, and as I said, it may be different depending on the state. But I would warn the OP or anyone reading this thread to consult a lawyer in their state about this -- because where I am, a family court judge, court advocate, and two different lawyers have said refusing visitation to the father, if he is listed on the birth certificate, can be used against the mother in any subsequent custody battles, and it can give the father MORE visitation than her. That's literally the first thing the court advocates said: "If he is on the birth certificate, denying him visitation is the worst thing you can do." That is the first question asked by lawyers and advocates - "Is he on the birth certificate?" Because if he is, that changes everything.
That doesn't come from a legal forum or website, but straight from the horse's mouth. So, again, maybe it's different depending on the state - I don't know. But any woman in the midst of a custody battle should speak directly to a lawyer herself before blocking visitation. Because she may end up shooting herself in the foot if she listens to this advice.
***It's also important to note that the website you linked to is not the website of an actual lawyer, but the equivalent of Wikipedia - anyone can post general information, that doesn't make it accurate. There is even a disclaimer at the very end stressing that the information listed "does not constitute legal advice."
I'm also confused about this idea that you can just put any man's name on the birth certificate on your own. I've never heard of that -- both where I am now, and where the baby was born before, you needed the man's signature if you put his name on the certificate. And if he wasn't there to sign, you'd need a notarized form with his signature on it. So his consent was required. Again, maybe this is just an issue of different jurisdictions, but in my experience it isn't possible to just list a name without the person providing his consent.