The jurisdictions are divided as some bishops remained in communion with Rome and other didn't. But that doesn't affect the apostolic authoirty transmitted through aposotlic succession of the bishops.
My reading of "Millers Church History" speaks to apostolic authority being a myth.. Jesus did not call Simon the first name Peter(as a nickname) he called him a rock.. metaphorically as an operator in the metaphor.. the church being rock upon rock.. starting from the cornerstone..
This metaphor getting skewed like the eat my flesh and drink my blood metaphor(Lords table) getting skewed all out of shape.. Its obvious these two metaphors are metaphors(to me/and others).. Stretching them to be literal makes them bizaar.. in the extreme.. Trans-substantiation is childlike and humorous in its skewing..