My child is a few months shy of turning 16 years of age. My child's biological father has not been a part of my child's life for the past twelve years other than an occasional phone call once/twice a year. The last twelve months, my child has not heard from this biological at all. My husband has been wanting to adopt my child and my child wants my husband to adopt but the biological would not sign the papers ten years ago. Can my husband and I petition the court to allow this adoption to take place on the permise of abandonement? How expensive would this process be to take place? Is there a better remedy for us?

Your ex will still be notified, and have the right to come to court and protest. So it is not going to be easy if he will not sign over his rights to adopt.
Attorneys all charge different rates, but my guess ( and a guess) they would start with a retainer of 5000, and go from there if there is a lot of court appearances.