The first thing you need to do is sit down with an experienced adoptions attorney in your area. Adoption is not something you really want to try to do on your own. It can be procedurally challenging.
The easiest way to get an adoption through is for the biological father to relinquish his rights. He may be willing to do so once he finds out that his current child support obligation would terminate when his parental rights are terminated. His past-due support is not affected by an adoption: he still will have to pay back support.
This is one of those areas where spending money on a lawyer is a really good idea. Make sure it's someone who primarily does adoptions.
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