(a) The Court of Criminal Appeals shall have final appellate jurisdiction coextensive with the limits of the state, and its determinations shall be final, in all criminal cases of whatever grade, with such exceptions and under such regulations as may be provided in this Constitution or as prescribed by law.
(b) The appeal of all cases in which the death penalty has been assessed shall be to the Court of Criminal Appeals. The appeal of all other criminal cases shall be to the Courts of Appeal as prescribed by law. In addition, the Court of Criminal Appeals may, on its own motion, review a decision of a Court of Appeals in a criminal case as provided by law. Discretionary review by the Court of Criminal Appeals is not a matter of right, but of sound judicial discretion.
(c) Subject to such regulations as may be prescribed by law, the Court of Criminal Appeals and the Judges thereof shall have the power to issue the writ of habeas corpus, and, in criminal law matters, the writs of mandamus, procedendo, prohibition, and certiorari. The Court and the Judges thereof shall have the power to issue such other writs as may be necessary to protect its jurisdiction or enforce its judgments. The court shall have the power upon affidavit or otherwise to ascertain such matters of fact as may be necessary to the exercise of its jurisdiction.