Texas Estates Code - EST § 113.153. Ownership of Trust Account on Death of Trustee

(a) If the account is a trust account and there is a written agreement signed by the trustee or trustees, on death of the trustee or the survivor of two or more trustees, any sums remaining on deposit belong to:

(b) If two or more beneficiaries survive, no right of survivorship exists between the surviving beneficiaries unless the terms of the account or deposit agreement expressly provide for survivorship between those beneficiaries.