Pope Clement I asserted the authority of Rome over the Church of Corinth as early as 69-90 AD. http://www.newadvent.org/fathers/1010.htm
Patriarch Ignatius I of Antioch referred to Rome alone as the "presiding church." http://www.newadvent.org/fathers/0107.htm
Saint Irenaeus of Lyons stated that it was necessary for all churches everywhere to agree with the Church of Rome, since it was founded by the Apostles Peter and Paul. http://www.newadvent.org/fathers/0103303.htm
Pope Victor I asserted Rome's authority over the churches of Asia. http://www.newadvent.org/fathers/250105.htm
Saint Cyprian of Carthage referred to Rome as the "chief church" and the "throne of Peter", from which sacerdotal unity takes its source. http://www.newadvent.org/fathers/050654.htm
Pope Stephen I asserted Rome's authority over the churches of Cappadocia. http://www.newadvent.org/fathers/050674.htm
Pope Dionysius I deposed Patriarch Paul of Antioch. http://www.newadvent.org/fathers/250107.htm
And that's just the ante-Nicene period.