Apostolic Succession refers to the ordination of a bishop by the laying on of hands of a validly ordained bishop. It refers to all the bishops, not just the pope. And, vacant sees are filled all the time.
Was it broken with the death of Blessed Pope John Paul II? Nope.
Apostolic Succession is the laying on of hands from the ordaining bishops to another the bishop being ordained in the Sacrament of Holy Orders.
The Sacrament of Holy Orders confers the three ranks: bishops, priests, and deacons.
The other titles and honors are not a part of Apostolic Succession/Holy Orders but, are given to those that have Apostolic Succession/Holy Orders. A bishop, usually bearing the title of Cardinal, is selected to be bishop of Rome and, therefore, has the title of Pope (in Latin: Papa).
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