It depends on where you look; for example, my belief in the coming Angelic Pontiff [St. Hildegard, Bls. Anna-Maria Taigi, Elizabeth Canori-Mora, Fr. Peré Nectou, Rosa-Colomba Asdente, Palma d’Oria, Jean-Édouard Lamy, Mariam Baouardy, Marie Martel, Marie-Julie Jahenny] indicates that all will reunite with Rome. According to Bl. Anna-Maria Taigi:
“After the three days of darkness, St. Peter and St. Paul, having come down from Heaven, will preach in the whole world and designate a new Pope. A great light will flash from their bodies and will settle upon the cardinal who is to become Pope. Christianity, then, will spread throughout the world. He is the Holy Pontiff, chosen by God to withstand the storm. At the end, he will have the gift of miracles, and his name shall be praised over the whole earth. Whole nations will come back to the Church and the face of the earth will be renewed. Russia, England, and China will come into the Church.”
Bl. Catherine of Raccogini relays a very important point:
"
There is no complete or perfect Council before the time of the coming of this Holy Pontiff whom we await for the future renewal of the Holy Church.”
With the statement that "There is
no complete or perfect Council before the time of the coming of this Holy Pontiff," we see that even in the height of the Roman Church, Councils are not "complete," because those outside of ecclesial communion with the Bishop of Rome are not given representation (with few exceptions: Lyon II, Basel–Ferrara–Florence); however after the coming of the Angelic Pontiff will bring them back into ecclesial communion, and allow complete / perfect Councils to take place. This is one of many, but it is the best example off the top of my head.
