I also wonder how administrative government will work for the actual (barony) holdings on the map: Will individual cities/castles still be republics/feudal? How will this work with theocratic temples? Can I also work to spread my house to barony-tier holdings, or just to full duchy-tier governorships?
What happens if the emperor or one of the holders of themes inherit a title outside the empire?
If the emperor inherits the kingdom of France does that realm change to an administrative government henceforth?
Will one of the theme holders become a feudal vassal if they inherit a duchy in, say, Croatia while they are landed within the empire?
Dear Paradox Staff, given that an Admin realm can have vassals that are not Admin, I find it strange that an independent ruler who swear fealty to the Byzantine emperor become a part of the Byzantine emperor's bureaucracy instantly.
I see a lot of questions like these. So let me take a moment and go a bit more into the nitty gritty details and explain how these type of situation works and clear things up.
Admin rulers can have vassals of any government type. Just like how feudal rulers have republic or theocratic vassals, so too can admin. On a barony level, we stick with the regular governments for the corresponding holding types. Meaning that temples will be held by theocratic rulers (unless you have lay clergy), cities by republics, and castles by feudals. There aren't any real major changes here.
Admin characters are allowed to hold both castles and city holdings without penalties, however, which allows you to freely revoke these holding types and keep them to yourself, or grant them to an admin character and have them rule over the holding instead. You can do however you see fit here. Arguably, it might be worth it to replace feudal or clan barony rulers and replace them with admin (because you will have more favorable obligations that way), while keeping theocratic and republic rulers for temples and cities.
As for how we manage titles. If an admin character inherits a title, that title will become a part of their "domain" if you will, and the ruler will keep being admin, but any vassals that go along with the succession will keep their governments as is. Rulers won't change government automatically. So let's say you inherit a feudal title (which could potentially happen but is very unlikely), the title itself will start using the ruler's new succession law, effectively making it a new theme (or governorship), assuming the tier of the title allows it. Counties won't really be affected by this, since we only treat duchies and kingdoms as "governorships". Only those titles will have access to the new mechanics of being a governor.
A similar behaviour applies to the swear fealty case mentioned previously. If a ruler swears fealty, they will retain their current government type when they become a vassal. Again, we don't change their government automatically. It's only if they already were to be admin that they instantly become a governor. Do note that an admin liege, will have tools at their disposal to manage vassals of other government types, and make them admin. But more on that in the next DD.