Tex. Finance Code § 95.103: ACCOUNT HELD BY FIDUCIARY.

(a) A savings bank or federal savings bank doing business in this state may accept a deposit account in the name of a fiduciary, including an administrator, executor, custodian, guardian, or trustee, for a named beneficiary.

(b) A fiduciary may:

(1) vote as a member as if the membership were held absolutely; and

(2) open, add to, or withdraw money from the account.

(c) Except as otherwise provided by law, a payment to a fiduciary or an acquittance signed by the fiduciary to whom a payment is made is a discharge of the savings bank for the payment.

(d) After a person holding a deposit account in a fiduciary capacity dies, the savings bank may pay or deliver to the beneficiary the withdrawal value of the account, plus earnings on the account, or other rights relating to the account, in whole or in part, if the savings bank has no written notice or order of the probate court of:

(1) the revocation or termination of the fiduciary relationship; or

(2) any other disposition of the beneficial estate.

(e) A savings bank has no further liability for a payment made or right delivered under Subsection (d).

Acts 1997, 75th Leg., ch. 1008, Sec. 1, eff. Sept. 1, 1997.