Randy,
Also, to treat such a complex subject as conciliarity and how it is particularly treated in the West in such a short post, does not do it the justice and attention it needs.
Moreso, it can be argue that the driving engine for Papal supremacy was to finally separate Church and State. Right before the Papal Schism the investiture controversies were a cancer in the Western Church. Because of the prominence of Rome throughout Church history, many northern European Bishops looked over the Alps (This is where the term ultra monstanist comes from) to Rome for support. That was not necessarily the case with France. The last place of resistance within the Church for Rome to supremely take over at the time. After the 11th century, Rome was finally making progress to bring all the Western Bishops under one Bishop (The Chair of Peter), so France was obviously a sore spot. Curiously enough, right before the Papal Schism, Pope Boniface VIII and Phillip IV of France engaged in a nasty strife. Which led to Pope Clement V to refuse to move to Rome and remain in Avignon, France. While there is no convincing evidence to specifically point to it, it is suspected that it was during Phillip the Fair’s reign that Gallicanism took a stronger hold in the Church. Gallicanism opposes Ultramontanism, in that it the power of Rulers and the State are comparable to the Pope’s.
So what Rome was fighting so hard to avoid, was at risk during this period.
At the end of this controversy, The Council of Constance 1414-18 produced a very interesting document:
Sacrosancta, 1415
In the name of the Holy and indivisible Trinity; of the Father, Son, and Holy Ghost. Amen. This holy synod of Constance, forming a general council for the extirpation of the present schism and the union and reformation, in head and members, of the Church of God, legitimately assembled in the Holy Ghost, to the praise of Omnipotent God, in order that it may the more easily, safely, effectively and freely bring about the union and reformation of the church of God, hereby determines, decrees, ordains and declares what follows: - It first declares that this same council, legitimately assembled in the Holy Ghost, forming a general council and representing the Catholic Church militant, has its power immediately from Christ, and every one, whatever his state or position, even if it be the Papal dignity itself, is bound to obey it in all those things which pertain to the faith and the healing of the said schism, and to the general reformation of the Church of God, in bead and members. It further declares that any one, whatever his condition, station or rank, even if it be the Papal, who shall contumaciously refuse to obey the mandates, decrees, ordinances or instructions which have been, or shall be issued by this holy council, or by any other general council, legitimately summoned, which concern, or in any way relate to the above mentioned objects, shall, unless he repudiate his conduct, be subject to condign penance and be suitably punished, having recourse, if necessary, to the other resources of the law. . . . (trans J. H. Robinson in University of Pennsylvania. Dept. of History: Translations and Reprints from the Original Sources of European history, published for the Dept. of History of the University of Pennsylvania., Philadelphia, University of Pennsylvania Press, Series I. Voll III:6 [1912], 31-32 )
Because there was more than one Pope claiming the Chair of Peter — the Council claimed full and complete authority. (Sounds familiar?

).
It after the dust settles that in the
6th Session 1439 Council of Florence we see the following:
We also define that the holy apostolic see and the Roman pontiff holds the primacy over the whole world and the Roman pontiff is the successor of blessed Peter prince of the apostles, and that he is the true vicar of Christ, the head of the whole church and the father and teacher of all Christians, and to him was committed in blessed Peter the full power of tending, ruling and governing the whole church, as is contained also in the acts of ecumenical councils and in the sacred canons.
And it is truly from here on forward that Rome’s supremacy begins to unfold. I’m not going to repost these documents.