We discussed the validity and liceity of the Sacraments, particularly Holy Orders, last time, noting that a church may recognize lineages of Apostolic Succession of bishops as having valid Holy Orders despite that lineage being outside that particular church. In short, the Church may recognize a man as a “real” bishop even if he was ordained irregularly. One way this can occur is though schism, pure and simple. That is, a bishop goes rogue and breaks away from the Church, then ordains as many men as he sees fit. Since the bishop was validly ordained in the Church, these ordinations he performs, though illicit and carrying the penalty of automatic excommunication for both the bishop himself and those he ordains, are valid. The men he ordains, in short, are real bishops, full stop.
We saw back here, though, that while some lineages indeed arose through schism (or in some cases, it would be better to say they were maintained despite schism), there are many small independent groups that were formed by individuals with their own ideas about how a sacramental church should be. Often there was no formal schism, and the founders of these groups sought out ordination to gain legitimate Apostolic Succession. How did they manage this? Through the phenomenon, mentioned but not described previously in this series, of wandering bishops.