Any person who claims as heir of any such decedent shall present his or her claim to the district court within ten (10) years after the appointment and qualification of the administrator, or such claim shall be forever barred. If such person establishes his or her claim it shall be allowed by the court. The court shall determine which of several claimants have established their claims and the share of the estate to which each is entitled. If at the time of such determination the estate is in the custody of the administrator, the same shall be paid or delivered to those adjudged entitled thereto, less claims previously allowed and prior demands and other items. If the proceeds of the estate have been remitted to the state treasurer, the secretary of revenue shall pay to those entitled thereto the sum or share of the estate the court has adjudged they are entitled to receive. No interest shall be allowed or paid thereon.