Justice Scalia passed away on February 13, 2016. Twelve days later, on February 25, 2016, the Supreme Court announced that Justice Thomas would serve as the Circuit Justice for the Fifth Circuit. (This appointment was temporary, as Justice Alito was later selected as the permanent Circuit Justice).
The Court still has not selected a new Circuit Justice for the Second Circuit. Would an emergency stay application form the Second Circuit still be addressed to Circuit Justice Ginsburg? That sort of caption is Reinhardt-esque.
My guess is that Justice Sotomayor, the native New Yorker, will get the nod for the Second Circuit. Justice Kagan, also a New Yorker, is lower on the list of seniority. And Justice Gorsuch will take over the Tenth Circuit from Justice Sotomayor. And, more likely than not, Justice Barrett will pick up the Eighth Circuit from Justice Gorsuch–close enough to Indiana. Unless Kavanaugh swaps with Barrett, and gives her the Seventh. Kagan, alas, is likely stuck with the Ninth Circuit for some time.