Apostolic succession applies to all successors of the original 12 apostles. Every modern day bishop and priest (including the Pope) has been ordained by Bishops, creating an unbroken lineage all the way back to the original 12.
This wikipedia section has it right, as far as I've read.
In Roman Catholic theology, the doctrine of apostolic succession
states that Christ gave the full sacramental authority of the Church
to the Twelve Apostles in the sacrament of Holy Orders, making them
the first bishops. By conferring the fullness of the sacrament of Holy
Orders on the apostles, they were given the authority to confer the
sacrament of Holy Orders on others, thus consecrating more bishops in
a direct lineage that can trace its origin back to the Twelve Apostles
and Christ. This direct succession of bishops from the apostles to the
present day bishops is referred to as apostolic succession.
And as it states, Papal Primacy, which is what you're hinting at, is a different but related matter.
The primacy of the Bishop of Rome is an ecclesiastical doctrine
concerning the respect and authority that is due to the Bishop of Rome
from other bishops and their sees.