St. Cyprian, bishop of Carthage in 250 published a teaching that from the time of St. Peter any church wanting to be accepted as part of the Catholic Church had to be in union with Rome. That contention has not always been universally accepted. There have been rocky times.
Although Emperor Constantine at the Council of Nicea had defended the belief that Jesus was the Son of God, his son Constantius, who came to rule in 337 rejected the findings of the Council of Nicea. His younger brother, Constans, kept the western half of the empire in union with Rome.
From 1309 to 1377 the popes, seated from Rome, pulled the Church from Avignon, France/
Then, in 496 the whole nation of the Franks, under king Clovis, were baptized. And, that Frank bishop, Remigius, without reference to Rome, was sn as the leader of the Christian nation.
The First Vatican in 1870 awarded the pope with universal jurisdiction throughout Catholicism, but from the time of St. Peter the jurisdiction of other apostles in their churches has been recognized.