If the father establishes his paternity of the child, you will not be able to have him adopted without the father's consent.
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I'd respectfully disagree with the sentiment that you'd be unable to have your Husband adopt without the father's consent. It is quite possible that the father has legally abandoned the child, in which case the Court can dispense with the need for his consent. Since more facts would be needed to assess this, you're best advised to schedule a consultation with a NYC Family Law attorney.
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You do need his consent to adopt if he could turn around and seek an order of filiation and some custody/visitation, but your story is a little mixed up there (if I understand it) that if you or he DID do this, then he WOULD have to pay child support.
Since he probably wants little to do with the child and doesn't want to pay child support, it is probably in his best interest to consent to a termination of parental rights and allowing your new husband to adopt. This is about the only situation, BTW, where he could terminate parental rights and NOT be potentially responsible for child support.
Unless this guy is suddenly demonstrating an interest in the child or is looking to pay child support, which most biological fathers in this position avoid like the third rail, since it will suck up much of his after tax income, he will consent to the adoption.
If he doesn't consent, you can possibly still succeed over his objection on a contested petition to terminate parental rights allowing your husband to adopt. But as I said, most biological parents in this position and with this little previous demonstrated interest in the child are only too happy to sign papers as fast as they can to avoid a possible child support obligation.
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