Can children receive an inheritance from a parent who waived their parental rights?

Ohio doesn't have any law that authorizes an parent to waive his/her parental rights. Parental rights can be terminated by a court - for abuse or neglect and parental rights are terminated if a child is adopted and an adoptive parent replaces the biological parent. But if the children were not adopted and no court ever terminated the father's parental rights, then as the father's biological children, they have the right to inherit - as long as the father died without a will. If a person writes a will, then the inheritances go as directed in the will. Without a will, children have the right to an inheritance. They might have to prove their relationship but with DNA testing that's simple today.