I'm in NYS. My neighbor adopted her cousin's child (birth mother eminently unfit). Both live in NYS. There were background checks, social services checks, a multitude of court dates--all of which were to check up on my neighbors and make sure that the child was in a good home now. My neighbor asked if social services could interview me. When the lady came, she was professional yet nice, asking me what I knew about my neighbors, how long I'd known them, etc. I realized that she was fishing to see if they were secretly running a meth lab in the basement or something like that.
It takes 7 years here for "denial of parental rights"--meaning the birth parents have no legal claim on the child anymore, and it's officially the adoptive parents' child now.
One of the potential hazards in the adoption process was any change in the financial circumstances of the adoptive parents--even positive ones. My neighbor's husband got a promotion at work just before the final court date. If he had mentioned that, the process would have stopped for yet another check! When they sat at a table with the lawyer, and the lawyer asked about changes, my neighbor kicked her husband in the shin so he'd say, "No changes."
The other problems they ran into was the birth mother not showing up for court dates, the who child protective court process taking hours each time--and no food or drink allowed in the courtroom. When the child was small, they had lots of trouble keeping the poor thing quiet and happy in the courtroom. One other problem was a clueless judge. At one court date, my neighbors and the birth mother were all there. The birth mother was strung-out and belligerent (I met the woman twice--scary), and my neighbors were, middle-class, respectable people. Despite that, the judge (not their usual one) said at one point, "But wouldn't the child be better off with its 'real' mother?" AARRGGHH.
That's what I remember. This all finiahed up 8 years ago. Hope it helps.