Do I have any custody rights over my adult child?

Generally not. The court cannot award custody of any child once that child has reached the age of 18. However, as a landlord or as a continuing contributor to your children, you can enforce any reasonable obligation in exchange for your doing more than the law requires of you. For example, if you pay only the minimum child support required by law, you will not be able to enforce any additional conditions against your children. However, if you pay more child support or pay for a longer period of time than the law would compel you, you may demand concessions from your children in exchange for that consideration.