[Mrs. Don-o]

By "passed them on," I suppose you mean, "Passed on the authority of his ministry" (since we are not talking about physical keys). After Peter's martyrdom in Rome, his successor was Linus. Here's the requested documentation:

Irenaeus: "The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate." Against Heresies 3:3.3

The Oxford Dictionary of Popes interprets Irenaeus as classifying Linus as the first bishop of Rome. J. N. D. Kelly, Oxford Dictionary of Popes, 2005

Linus is presented by Jerome as "the first after Peter to be in charge of the Roman Church""Post Petrum primus Ecclesiam Romanam tenuit Linus" -Chronicon; 14g (p. 267)

Eusebius calls Linus "the first to receive the episcopate of the church at Rome, after the martyrdom of Paul and Peter" Church History 3.2

John Chrysostom wrote, "This Linus, some say, was second Bishop of the Church of Rome after Peter",Homily 10 on 2 Timothy

The Liberian CatalogueThe Chronography of 354 AD. Part 13: Bishops of Rome presents Peter as the first Bishop of Rome and Linus as his successor in the same office.

[MamaB]

Just because a writer says, “ some say” does not make it true.

[ealgeone]

Eusebius calls Linus "the first to receive the episcopate of the church at Rome, after the martyrdom of Paul and Peter" Church History 3.2

This only records what happened at Rome and does not mean Rome ruled the rest. If you read Eusebius you will see that he did not recognize Rome as "the" official seat.

You're cherry-picking again.

[BlueDragon]

The Oxford Dictionary of Popes interprets Irenaeus as classifying Linus as the first bishop of Rome. J. N. D. Kelly, Oxford Dictionary of Popes, 2005

All hail the bishop of Rome!

And the bishop of Alexandria, and the one at Antioch, Jerusalem, and every other bishop. Hail all.

Yeah, I know... that may slow or interrupt the "hail Mary(s)" a bit, but sacrifices must be made, eh?

[CynicalBear]

All hearsay and quoted or repeated hearsay. Peter never had a successor nor was He the bishop of Rome. In fact, it's a proven reality that there was no single authority in Rome until after Constantine.