...definitions of "Church" and "apostolic succession" would be a necessary starting point [to determine how Protestants had authority to break away from the Church during the "Reformation"]. Things like that tend to break down in view of the structure of the early church anyway.
I think thefrankbaum gave a reasonable definition of apostolic succession, and what it means, and also showed that it was indeed part of the "structure of the early church". As far as a definition of "Church" itself, classically, it's the "Body of Christ" and, at the same time, the "Body (or group) of Believers".
I would prefer you continue conversing with thefankbaum, specifically, responding to his post #349 to you. Even more specifically, to answer the question, "Further, what do you think the reason for the laying on of hands (especially in the case of Paul) was, if not to pass along this authority?"
There is no evidence that this is exclusive to a specific set of Christians. It wasn't just a few who received the gifts of the Holy Spirit as evidenced in Acts 2:4, Acts 10:47, and 1 Cor. 16:9 and especially in 1 Cor. 14:26. Passing on of the Holy Spirit is through laying on the hands as in Acts 8:17 and Acts 19:6. So if laying on the hands and receiving the Holy Spirit is evidence of authority, then all Christians have this authority.