Definition of the Branch Theory

…the theory that, though the Church may have fallen into schism within itself and its several provinces or groups of provinces be out of communion with each other, each may yet be a branch of the one Church of Christ, provided that it continues to hold the faith of the original undivided Church and to maintain the Apostolic Succession of its bishops. Such, it is contended by many Anglican theologians, is the condition of the Church at the present time, there being now three main branches, the Roman, the Eastern, and the Anglican Communions… From the Oxford Dictionary of the Christian Church