This must be the single most obscure feature of the game. What *do* these people do? Clearly, a lot of them are actually historical characters (Patriarchs of non-Catholic Eastern Churches, for example), so I am very interested as to whether they have any role to play once they appear.
The most they can do is to give support to their heresy, which is so helped in spreading all around thanks to the presence of her "founder". In fact they cannot do conversions.
But how do they do that? Do they give some kind of a local/global bonus to conversions, or is it something else? Or, for example, would they make non-heretical missionaries less effective in the province where they are stationed?
They mostly provide a defensive bonus to their heresy (hence making the heresy more difficult to eradicate), in addition to a chance the heresy spreads nearby...