The Volokh Conspiracy
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Larry Seltzer asked this question via Twitter, so I thought I'd answer it.
First, some background: Each federal circuit has a Supreme Court justice assigned to it. That justice's job is to deal with applications for stays of lower court judgments generally, stays of execution in particular, extensions of time and other procedural matters coming out of that circuit. Some such matters, such as stays, can be quite important, though the most important ones tend to be referred by the circuit justice to the entire court. A federal statute provides that the justices will assign the circuits by court order, and a 2010 order provided that Justice Antonin Scalia would be in charge of the U.S. Court of Appeals for the 5th Circuit, which covers Louisiana, Mississippi and Texas.
Now, the answer to Seltzer's question: Justice Anthony M. Kennedy, because he was the justice appointed after Scalia. Supreme Court Rule 22.3 provides that:
When the Circuit Justice is unavailable for any reason, the application addressed to that Justice will be distributed to the Justice then available who is next junior to the Circuit Justice; the turn of the Chief Justice follows that of the most junior Justice.
But I assume that the Supreme Court will soon issue a new formal order reassigning the circuits, in whatever way the justices prefer.
UPDATE [Feb. 26, 2016]: Yesterday, the Court did issue a new circuit allotment order; Justice Thomas was assigned to the Fifth Circuit; he is also the Justice responsible for the Eleventh Circuit.