I just adopted the wife's daughter. The longest time was the process. Took about 4 months from start to finish. We had to notify the sperm donor, have a court date to see if he would try to interfere, and then a court date where we went in front of the judge to sign the paperwork. I got asked a few questions. Name, is the home big enough for the children, if I wanted her name changed, if I could financially support her, and things of that nature. Wife had to basically say she agrees, and that was it. Judge gave our daughter an adopted teddy bear and a few coloring books and other little toys. Took maybe 10-15 minutes in court.
If it takes a while to find sperm donor and serve him papers, it will take longer, same as if he wants to fight the adoption. But the first court date, the Judge pretty much told him he had no rights in my case. Never saw her, no child support, no attempt to do anything with her.