(a) If the account is a P.O.D. account and there is a written agreement signed by the original payee or payees, on the death of the original payee or on the death of the survivor of two or more original payees, any sums remaining on deposit belong to:
(1) the P.O.D. payee or payees if surviving; or
(2) the survivor of the P.O.D. payees if one or more P.O.D. payees die before the original payee.
(b) If two or more P.O.D. payees survive, no right of survivorship exists between the surviving P.O.D. payees unless the terms of the account or deposit agreement expressly provide for survivorship between those payees.
(c) A guardian of the estate or an attorney in fact or agent of an original payee may sign a written agreement described by Subsection (a) on behalf of the original payee.