The only leg left for the theory of Apostolic Succession is the ordination process, with the laying on of hands. However, it seems that if the Apostles did not directly appoint the next generation of Bishops than the laying on of hands being valid is not dependent upon them, but rather the individuals laying on hands being indwelt by the Holy Spirit.
If this is correct, than any Christian body of believers has a valid ordination process as long as those laying on hands are indwelt by the Holy Spirit.
All that the laying on of hands did was recognize that the candidate was called by God to the office or mission. It conferred nothing. The Clement letter (ca. 85-90 A.D.) and Didache set out the "tradition", however Acts 13:3 gives us the scripture.