An anti-pope is a claimant on on See whose claim is to some extent legitimized by his ordination by acting bishops/cardinals present in those positions. They are defined as non-official largely because there were two Papas sitting in different places at the same time, which ain't allowed.
It is you who do not understand. If an anti-pope is elected by a significant number of dissidents, that does not de-legitimize, the Petrine Succession. It may make it cloudy as to who is in line, but in terms of legitimacy, it matters not. It's similar as to when we had a discussion as to which came second or third in the rolls of the See of Antioch. I don't think that you get that it is not
the person, handing the office off to the next guy in line, that makes for the "Succession". Please read that again, so you get the importance of that. I really don't know if Linus was second or third or if Clement was third or forth as the Bishop of Rome. It doesn't matter in the end. It has little to do with the validity of Succession. Validity is conveyed by whether that person, no matter where they were in line, was validly ordained or consecrated into that position
, i.e., by those or someone who has the proper authority to do so
. It is the bold end of that last sentence that is key. Protestants can use the exact form of ordination as Catholics or Orthodox, but all who they ordain, and who those in turn ordain, are completely invalid. Scripture is crystal clear on this. This is what you do not seem to understand about Succession, Petrine or Apostolic. This is why I keep asking you, "Where do Protestants get their authority?" It is because Holy Scripture makes abundantly clear that the only ones authorized to bequeath authority in the Church are those who have themselves been properly ordained. This is why even Paul, called directly by Christ, went to Jerusalem to be ordained. He ordained Timothy as Bishop. Timothy ordains Presbyters in various cities. It is the only valid model. This is why the visible Church, the Apostolic Succession and the united priesthood with Christ has been deemed so vital by the Holy Christian Church for two thousand years, whether Catholic, Eastern Orthodox, or Coptic. It simply cannot be gotten around in the NT, which is where I began to have serious doubts about the intellectual defensibility of Protestantism during my youth. That the anti-Popes may ordain many Bishops or Presbyters is possible. It effects nothing. Their ordinations are still, if properly done, valid. Hence the Eastern Orthodox Succession is still valid with us. The actions of their Bishops and priests may be illicit, however. Clear?, or more clear?
Tell me, how can one be a legitimate bishop of Rome, without ever stepping foot in Rome?
The same way that when President Johnson was sworn in in Texas...he was validly the President. FYI; The Pope, who by virtue of being the Bishop of Rome, is
the Pope, has not lived in Rome since 1929. He not only does not live in Rome, he does not even live in Italy. He resides in the State of Vatican City. A completely sovereign and independent country from Italy.
Really? When the entire presbytery of the See is compromised to the extent that one can buy or blackmail a candidate into "Peter's chair," you don't see a discontinuation, a "disappearance" as you said, of the church there?
If it did, then our Lord's promises about His Church were lies. Absolutely not! This is the major point you Protestants do not get about the Church. The priesthood is sacrosanct, as Christ promised us. His Church is his Body, and impervious to the sins of man in regards to faith and morals, i.e., the dogma, doctrines, teachings and Sacramental validity of the Church. Why stop at the Medici's? Every single, Bishop, Priest, Deacon, and Christian, on the face of this earth, since Peter denied Christ three times, has been, and will be, a terribly flawed and bastard sinner, who deserves no salvation...and yet it is there for the asking, nevertheless.
I'll happily take the correction if I'm wrong, but AFAIK dying while excommunicated precludes salvation, does it not?
Assuming we know the full mind of God on the subject of that person, then yes, it does, which is why I agree with you, that although it is a bit more complicated than we are putting here, if one dies in an unrepentant state of mortal sin, and one is excommunicated, then off to the nether regions of Hell doth one go. That is why it is considered a "corrective" and temporary measure requiring a particular grave situation. I have never heard of it being used personally, although if one commits abortion willingly, you could be excommunicated automatically in some Dioceses that I have heard of.