According to Ohio 2108.81 Right of disposition—no declaration of assignment
(A) If either of the following is true, division (B) of this section shall apply:
(1) An adult has not executed a written declaration pursuant to sections 2108.70 to 2108.73 of the Revised Code that remains in force at the time of the adult’s death.
(2) Each person to whom the right of disposition has been assigned or reassigned pursuant to a written declaration is disqualified from exercising the right as described in section 2108.75 of the Revised Code.
(B) Subject to division (A) of this section and sections 2108.75 and 2108.79 of the Revised Code, the right of disposition is assigned to the following persons, if mentally competent adults who can be located with reasonable effort, in the order of priority stated:
(1) The deceased person’s surviving spouse;
(2) The sole surviving child of the deceased person or, if there is more than one surviving child, all of the surviving children, collectively.
And elsewhere in the statutes, the “Right to Disposition” is defined as:
(1) The right to direct the disposition, after death, of the declarant’s body or any part of the declarant’s body that becomes separated from the body before death. This right includes the right to determine the location, manner, and conditions of the disposition of the declarant’s bodily remains.
(2) The right to make arrangements and purchase goods and services for the declarant’s funeral. This right includes the right to determine the location, manner, and condition of the declarant’s funeral.