Your nephew is no longer a minor and quite capable of looking after himself. He's considered an adult now so the normal adoption process that would be used for a minor doesn't apply here. However, if there are other factors, and your nephew has no family or has disowned his parents, he is of age to go with you before the justice system and have you adopt him. It's a matter of who he considers his family and what strength that will give him in his character than anything else. It also would give him a sense of belonging. Ask your nephew what he thinks of this and if it both makes you feel better to do so, then seek out legal advice and start the ball rolling.AnswerAs the previous answer stated, your nephew is 20 years old and is considered a legal adult. If there are no other mitigating factors, there is no adoption issue. However, if he is in any way disabled and cannot care for himself and requires a guardian or trustee, then that would require the normal court process to show that you are more capable of caring for his needs than his biological parents.
Both the answers above came to you from people who do not know adoption laws, otherwise they would have known that children are considered "adoptable" through the age of 21 years old, and "special needs" adults (such as with Autism or Downs Syndrome, etc) are adoptable for as long as they live no matter how old they are. But as mentioned above, go to your local court and ask for advice from a family services lawyer/counselor as to how to proceed. Also contact your state Department of Human (Child/Family) Services as they would be the ones who would have to handle all the actual paperwork.