Recently, I've experimented on what causes personal unions (PUs) to happen or not; and from the information I've gathered, the rules that I believe to be in play are consistent (100% of the time from what I have tested) in the short term (a year from november 1444 to january 1446).
I have tested with two nations, Gelre and Austria, both of which begin the game without any heirs.
First off, if you only do one royal marriage, the main element which seems to determine PUs is score. If you marry someone who is ranked 12th or above, you will have a PU under them if your ruler dies without any heir; if you do the same with a nation who is ranked 13th or below, you will only get a noble from their house. The size of the nation does not matter ; only the score does.
Moreover, the order of marriages you do matters : if you first marry a nation whose rank is 13th or below, and afterwards marry a nation whose rank is 12th or above, you will get a noble from the house of the nation with the highest score.
Your own score doesn't affect anything on the outcome of your own succession: if Austria marries France, for instance, it will form a PU under France if their monarch dies heirless; and same would go for Gelre if it married France.
For the short term (a year from november 1444 to january 1446) - I haven't experimented more -, prestige only affects the outcome of a succession depending on how much a nation has when it does the royal marriage. I do not know what determines the amount of prestige necessary to affect the outcome of a succession, but if you have much more prestige than the nation you marry, regardless of their score, you will only get a noble from their house - for instance, if Gelre marries into Austria with a prestige of 84 or more, it will only get a Habsburg noble. For the short term (a year from november 1444 to january 1446), the fluctuations of prestige don't change anything : if at the time you married Austria, for example, you had a 100 prestige, and get a Habsburg noble upon your monarch's death, if the day after you have -100, you still get a Habsburg noble.
Prestige doesn't seem to affect the outcome if you marry nations whose rank is 13th or below : you still get a noble from their house as a result.
The tech group doesn't affect anything, you can have a PU under a nation who is eastern tech as a western nation, for instance.
Finally, the outcome changes accordingly to the variations of score: if you marry a nation whose score is 13th, and your succession is a noble from their house, and afterwards they move up to 12th in score the following month, you will have a PU under them.
EDIT: I forgot to add that, if you are in a war that involves the one under who you will be in a PU upon succession, for the duration of the war, if your monarch dies without an heir, you will have a noble from their house instead. For instance, if Gelre marries France at the beginning of the game, they will be under a PU with France if their monarch dies ; however, if they enforce peace on England to join the HYW, for the duration of the HYW, they will have a noble from house de Valois instead of falling under a PU with France.
I have tested with two nations, Gelre and Austria, both of which begin the game without any heirs.
First off, if you only do one royal marriage, the main element which seems to determine PUs is score. If you marry someone who is ranked 12th or above, you will have a PU under them if your ruler dies without any heir; if you do the same with a nation who is ranked 13th or below, you will only get a noble from their house. The size of the nation does not matter ; only the score does.
Moreover, the order of marriages you do matters : if you first marry a nation whose rank is 13th or below, and afterwards marry a nation whose rank is 12th or above, you will get a noble from the house of the nation with the highest score.
Your own score doesn't affect anything on the outcome of your own succession: if Austria marries France, for instance, it will form a PU under France if their monarch dies heirless; and same would go for Gelre if it married France.
For the short term (a year from november 1444 to january 1446) - I haven't experimented more -, prestige only affects the outcome of a succession depending on how much a nation has when it does the royal marriage. I do not know what determines the amount of prestige necessary to affect the outcome of a succession, but if you have much more prestige than the nation you marry, regardless of their score, you will only get a noble from their house - for instance, if Gelre marries into Austria with a prestige of 84 or more, it will only get a Habsburg noble. For the short term (a year from november 1444 to january 1446), the fluctuations of prestige don't change anything : if at the time you married Austria, for example, you had a 100 prestige, and get a Habsburg noble upon your monarch's death, if the day after you have -100, you still get a Habsburg noble.
Prestige doesn't seem to affect the outcome if you marry nations whose rank is 13th or below : you still get a noble from their house as a result.
The tech group doesn't affect anything, you can have a PU under a nation who is eastern tech as a western nation, for instance.
Finally, the outcome changes accordingly to the variations of score: if you marry a nation whose score is 13th, and your succession is a noble from their house, and afterwards they move up to 12th in score the following month, you will have a PU under them.
EDIT: I forgot to add that, if you are in a war that involves the one under who you will be in a PU upon succession, for the duration of the war, if your monarch dies without an heir, you will have a noble from their house instead. For instance, if Gelre marries France at the beginning of the game, they will be under a PU with France if their monarch dies ; however, if they enforce peace on England to join the HYW, for the duration of the HYW, they will have a noble from house de Valois instead of falling under a PU with France.
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