How bad were the circuits' opinions?  So bad the habeas petitioners made little or no attempt to defend them. 

Gonzales barely defends the Ninth Circuit's interpretation of §3599. He offers a single, halfhearted argument in support of the Ninth Circuit's opinion based on our statement in McFarland v. Scott, 512 U. S. 849, 858 (1994),that "the right to counsel necessarily includes a right for that counsel meaningfully to research and present a defendant's habeas claims." 

In the Ohio case:

We would address Carter's arguments in defense of the Sixth Circuit's decision, but, there are none. Carter's brief informed us that "[t]his Court need not consider the statutory argument with which the [petitioner's] brief begins--i.e., that there is no 'statutory right' under 18 U. S. C.§4241 to be competent in habeas proceedings." Brief for Respondent in No. 11-218, p. 15. Apparently, Carter found the Sixth Circuit's reasoning indefensible. We agree.

Having disposed of the reasons the two circuits actually gave, the Court goes on to discuss in general terms when a habeas court can issue a stay due to incompetency of the petitioner.  In a criminal trial, of course, the defendant cannot be tried while incompetent.  He needs to be able to assist his lawyer with matters within his own knowledge, such as where he really was at the time of the crime or, if he was at the scene, what really happened.  Simplistically applying the same rule to habeas overlooks the fact that collateral review is further removed from the facts of the original case, and federal habeas for state prisoners is another step removed.

Encouragingly, the Court strongly reaffirms its landmark Pinholster decision:

Given the backward-looking, record-based nature of most federal habeas proceedings, counsel can generally provide effective representation to a habeas petitioner regardless of the petitioner's competence. Indeed, where a claim is "adjudicated on the merits in State court proceedings," 28 U. S. C. §2254(d) (2006 ed.), counsel should, in most circumstances, be able to identify whether the "adjudication . . . resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," §2254(d)(1), without any evidence outside the record. See Cullen v. Pinholster, 563 U. S. ___, ___ (2011) (slip op., at 9) ("[R]eview under [28 U. S. C.] §2254(d)(1) is limited to the record that was before the state court that adjudicated the claim on the merits. . . . This backward-looking language requires an examination of the state-court decision at the time it was made. It follows that the record under review is limited to the record in existence at that same time--i.e., the record before the state court"). Attorneys are quite capable of reviewing the state-court record, identifying legal errors, and marshaling relevant arguments, even without their clients' assistance.

This reaffirms the understanding of Pinholster that too many federal courts have been disregarding.  Proceeding straight to the decision of the 2254(d)(1) question with no further factual development is supposed to be the norm.

So as to claims that can be resolved on the state court record under 2254(d), the Arizona district court was right to proceed, and the Ohio district court incorrectly granted a stay.  "Any extrarecord evidence that Carter might have concerning these claims would therefore be inadmissible. Pinholster, supra, at ___. Consequently, these claims do not warrant a stay."

If a claim does allow extrarecord evidence, and the petitioner is unable to give assistance he might give if competent, a stay might be in order, but only a temporary one if there is a chance competency might be restored.

But even if Carter could show that the claim was both unexhausted and not procedurally defaulted,¹⁷ an indefinite stay would be inappropriate.... "Staying a federal habeas petition frustrates AEDPA's objective of encouraging finality by allowing a petitioner to delay the resolution of the federal proceedings." Rhines, 544 U. S., at 277....  At some point, the State must be allowed to defend its judgment of conviction.¹⁸

If a district court concludes that the petitioner's claim could substantially benefit from the petitioner's assistance, the district court should take into account the likelihood that the petitioner will regain competence in the foreseeable future. Where there is no reasonable hope of competence, a stay is inappropriate and merely frustrates the State's attempts to defend its presumptively valid judgment.

Footnote 17 notes that Pinholster did not address the boundary between a new claim and a previously adjudicated claim.  Footnote 18 notes that competency to be executed is a different matter.

This is a big win for the cause of justice.  Congrats to our friends at the Arizona and Ohio Attorneys General offices.