Texas Code of Criminal Procedure - CRIM P Art. 33.011. Alternate jurors

(a) In district courts, the judge may direct that not more than four jurors in addition to the regular jury be called and impaneled to sit as alternate jurors.  In county courts, the judge may direct that not more than two jurors in addition to the regular jury be called and impaneled to sit as alternate jurors.

(b) Alternate jurors in the order in which they are called shall replace jurors who, prior to the time the jury renders a verdict on the guilt or innocence of the defendant and, if applicable, the amount of punishment, become or are found to be unable or disqualified to perform their duties or are found by the court on agreement of the parties to have good cause for not performing their duties.  Alternate jurors shall be drawn and selected in the same manner, shall have the same qualifications, shall be subject to the same examination and challenges, shall take the same oath, and shall have the same functions, powers, facilities, security, and privileges as regular jurors.  An alternate juror who does not replace a regular juror shall be discharged after the jury has rendered a verdict on the guilt or innocence of the defendant and, if applicable, the amount of punishment.