Paper-thin Ecclesiology

I have just had an image that I thought I ought to share. Ingredients: Two pieces of paper and some superglue. Recipe: Put one paper on top of the other so that there is a 1'' overlap. Glue. Wait for glue to set hard. Now pull the papers apart again. What's the result? In my fevered imagination: a vision of Ecclesia Anglicana and Ecclesia Romana. The gluing represents the Synod of Whitby (664 AD) whence the Holy See and the Anglican Church were joined. The tearing represents the Schism of the Reformation

Case 1: The papers separate undamaged (i.e. glue did not set). Thus the Reformation was not a Schism, but a separation of two distinct churches. An end to an entente cordiale.

Case 2: The papers separate but only one is damaged. In this case, one of the churches was damaged by the Schism, resulting in some loss of doctrinal, political or logistical integrity.

Case 3: Both papers incur damage. Each church needs the other to become whole again, because each possesses part of the other.

Where this model falls down is that pieces of paper do not grow, unlike the Church. However it does illustrate well the untidiness of the situation. In models 2 and 3, the rent that exists is potentially damaging, for here infection (thanks Mr. Goings and the Youngfogey for this elaboration) may be introduced, causing gangrene and sickness and further institutional instability. This is certainly evident in the Church of England, less so in the Roman Church.

Where do you fit on this issue?