If somehow the latin pope and all its bishops and all its clergy and millions of laity suddenly decided they were wrong their parents were wrong their grand parents were wrong their great grand parents were wrong their great grand parents were wrong ect ect ect and that their church and their saints were all wrong for the past 1000 years, I do not see why it is wrong to say Rome would have complete authority at least over Europe in her traditional boundaries, except of course for autocephalous churches already established such as the Church of Greece and the like.
I think it would be a terrible thing if Rome, while having those boundaries, would have to also share it with the Patriarchate of Constantinople and other jurisdictions. IT would just set up the same problem as in America, which is nonsensical idea and uncanonical anyway (how many times to say it! more than one bishop to a city is against the canons!)
As to the New World, I would think either Rome would keep it (Since the Ecumenical Patriarchate already admits that the Bishopric of Rome had the same kind of "universal jurisdiction" that the Ecumenical Patriarchate has) or that new patriarchates or something would have to be established, some kind of jurisdictional unity. This is of course assuming by then we would have solved our jurisdictional problem in America.
Of course, if it actually happened, this is not how it would work. there would just be a hogpog of jurisdictions and a complete mess of disunity and disorginization like in the US since pride is a powerful sin