I believe universal acceptance is determined by the cardinals and then the ordinaries of the Church. Are they united in the acceptance? Even that unity doesn't have to be 100% I believe, but a moral unanimity. I think Xavier Sem posted some authorities on this, but his posts are gone. We should check on this.
If indeed that is the standard, the Conciliar popes were universally accepted.
See my previous post. UA seems to be tossed out there all the time as if it were some given, dogmatically established. I disagree. It's a theological speculation that's fraught with difficulties, contradicted by the cuм ex, undermined by some historical precedents, etc.
And another aspect is ... universal by WHOM? 90%+ of Novus Ordites, by their own polls, have lost the faith, denying one dogma or another. So, if the Arians, which some have suggested took about 90% of the Catholic Church down in its day, had managed to elect an Arian as pope, would that 90% acceptance count for anything?
So of those Catholics who have still the faith, a very significant percentage, even if they aren't SVs, entertain serious positive doubt about the legitimacy of the V2 papal claimants. It is not necessary to be certain that they're illegitimate. Rather, if you're NOT certain, with the certainty of faith, that they're legitimate, if you can't basically say that you're as sure that Bergoglio is pope as that there are Three Persons in One God, then you don't have the requisite certainty of faith to make their legitimacy dogmatic fact, which is what it must be for any dogmas these popes were to define to be certain with the certainty of faith ... and that's where this principle of
Papa Dubius Papa Nullus ("a doubtful pope is no pope") come into play.