It's hard to believe the other country's nobles/bureaucracy reacting like "hey now this guy from house of whoknowsit some 300 miles away is our ruler let's transfer the collected tax to him and wait for his instructions on anything we do" so there must be some power consolidating thing like installing your nobles/bureaucrats in the new country, both on the political level and "business" level I guess?

Or, instead of properly ruling, maybe the ruler might sign an agreement with the establishment of the other country that they may keep doing what they've been doing so long as they pay some ducats as tax to the "ruler"?

Also, if the inheriting ruler was too weak compared to the inherited country or too distant from it, was it common for the inherited country to remain de facto "independent"? Who typically ruled the inherited country then and what were their standing, international politics-wise? Were they considered a "usurper"?

First time poster, please correct me if I do anything wrong. Couldn't find the answer in the FAQ. Thanks!

Edit: clarified part of question.