luitzen said:
How does a diocese bishop contribute to your realm?
Diocese bishop modifies and triggers events. Besides that, if he has a diplo-skill above 7, he does influence children's ecclesiastical education by his personal stats.
Also if you control pagan/muslim/jewish provinces they can help converting it.
From another thread I found this description:
One proper diocese bishop should be a martial cleric, who is not zealous, sceptical, heretic, or excommunicated, and who has a good health (doesn't have illness, pneumonia, or plagueinfested as traits). He should have loyalty above 90% and piety above 10. It also helps (but isn't required necessarily), if he has a diplomatic value at least 7, and at least some positive personality traits (such as energetic, reckless (very good!), temperate, valorous, wise, just, honest, generous, merciful, forgiving). And it's preferable, if he doesn't have too much negative traits (like coward, lazy, indulgent, vengeful, arbitrary, maniac (very bad!), indulgent, cruel, proud, selfish). All this influences diocese bishop's capability to get the conversion job done.
A bishop who is heretic can start converting your courtiers, it can be fun but not the best thing for your kingdom

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But usually the pope will send you lazy, lustful, sceptical guys

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