the lot fell upon Matthias
"Amongst those various offices which have been exercised in the Church from the earliest times the chief place, according to the witness of tradition, is held by the function of those who, through their appointment to the dignity and responsibility of bishop, and in virtue consequently of the unbroken succession going back to the beginning, are regarded as transmitters of the apostolic line."
-- CCC 1555
Thus the risen Christ, by giving the Holy Spirit to the apostles, entrusted to them his power of sanctifying: they became sacramental signs of Christ. By the power of the same Holy Spirit they entrusted this power to their successors. This "apostolic succession" structures the whole liturgical life of the Church and is itself sacramental, handed on by the sacrament of Holy Orders.
-- CCC 1087