Generally, an adult can leave his property to anyone he wishes, in a will. If a will is executed appropriately under state law and its terms are clear, probate courts must enforce it. Even minor children for whom the parent pays child support usually have no right to estate assets, if the parent does not provide for it in his will.
Many state laws protect children from accidental disinheritance. This comes into play when a parent makes a will that leaves property to the children he had when he wrote the will. If he has children after the will is executed and never revises it, the law presumes that the disinheritance of later-born children was accidental.
Some states, like Florida, have laws that give minor children the right to inherit homestead property that belongs to a parent. Under the Florida constitution, if the parent writes a will leaving the homestead property to another person, the devise fails and intestate laws apply, giving the surviving spouse a life-estate and the minor children the remainder.