Catholics: did the truly vile Borgia and Medici popes destroy apostolic succession?

No.

Apostolic succession is not affected by the character of the people who are part of the succession.

So they proposed two, Joseph called Barsabbas, who was also known as Justus, and Matthias. Then they prayed, "You, Lord, who know the hearts of all, show which one of these two you have chosen to take the place in this apostolic ministry from which Judas turned away to go to his own place." Then they gave lots to them, and the lot fell upon Matthias, and he was counted with the eleven apostles. (Acts 1: 23-26)

Apostolic succession means both fidelity to the faith of the apostles and assurance of that fidelity through historical continuity in the laying on of hands in episcopal (bishop) ordination.

Through the laying on of hands, new bishops become members of the college of bishops and successors to the apostles, sharing in their authority to teach, sanctify and rule.

For more information, see:

http://www.catholic.com/library/Apostolic_Successi...

http://www.newadvent.org/cathen/01641a.htm

http://www.scripturecatholic.com/apostolic_success...

With love in Christ.

Apostolic succession applies to the Church, not to the Papacy alone. All clergy are ordained by successors to the apostles. All confirmed Cathilics are taught by a successor to the Apostles. The Holy Spirit guides the Church as had been done since the first Pentecost.

God is stronger than evil. God is faithful to his Church even if many of us, even Popes, are unfaithful to him. For other examples read the OT.

they did not destroy the succession . they were certainly evil , but they never changed the teachings of Christ , the holy spirit guides the church in the teachings, and no false teachings have been attributed to the catholic church dealing with "faith and morals." Christianity is full of sinners and always will be . as jesus said in matthew 28;20 . "I will be with you until the end of time ." he only built the one church.

We have a Pope.