Can ecumenical patriarch permanently hold all pentarch titles?
I read on CK2 wiki that ecumenical patriarch can also hold multiple pentarch titles at the same time if desired (http://www.ckiiwiki.com/Autocephaly#Pentarchs), and that this can be used to extend the ecumenical patriarch's authority over multiple de jure patriarchal regions. I have always wondered how I could make the ecumenical patriarch be the religious head of all my subjects as the Byzantine emperor, but granting the pentarchy titles to the ecumenical patriarch hadn't occurred to me.
Following this strategy do the pentarchy titles on succession pass to the next ecumenical patriarch or do they have separate elections (thus negating the benefits the moment the ecumenical patriarch dies)?
I'm pretty sure the game doesn't let you do this. As Byzantine Emperor, I tried to grant the Bishopric of Alexandria to the Ecumenical Patriarch after I captured it in a holy war, but it wouldn't let me. It didn't even show up in the list titles. I could give him any other bishopric in the Duchy of Alexandria, and I could give the bishopric to someone else, but I couldn't give it to him. It looks like the wiki is out of date and the game now forces the pentarchs to be separate characters.
There is something you can do: conquer the specified target, as Alexandria. Now, you must own both the province and the Bishopric of Alexandria. Make the Bishopric your primary title then give the county of Alexandria to your Ecumenical Patirach.