How can a parent disown an adult child legally?

When you say "disown," from an estate planning perspective I believe you are referring to "disinherit." If this is the case, in your estate planning documents simply mention that it is your intention to disinherit your child named (insert child's full name) and that you have intentionally made no provision for that child. You have no obligation to provide anything for a child who is an adult. You cannot relieve yourself of the duty to support any minor children, however.