While theologies can tell us much about alt-Christianities, looking at practice is interesting, too. The question of Arianist monasteries has already been brought up. I find groups like the Agonistici and the Paulicians, who had less monepiscopal structures and were more political at the same time rather interesting. They may never have become hegemonial and stayed that way, but I wonder how Middle Ages might look where such groups had left a stronger imprint...