I have a collection of rare, odd, and unique things in my current game, without my intervention.
So here is my Europe:
Pretty much impossible to spot everything weird, so let's zoom on some unique things:
Independant Armagnac, allied to OPM Britanny and OPM Aragon. They survive untouched there since more than 100 years, between France and Castile. France lost their cores there and none of the 2 powers are interested in Armagnac so they might actually survive forever.
Independant Catalonia allied to Castile and holding the provinces preventing them from forming Spain.
Portugal being bigger than Castile.
Reformed France having a PU on Orleans, who only owns Valois and not Orléans.
The Pope enjoying the Baleares. Also a nice Two Sicilies holding Corsica and Sardinia... and...
The Emirate of Sardinia basically being Tunis.
All of this chaos actually comes from one single thing: Aragon got a PU on Castile in 1446, which France contested and lost. That led to a French explosion and to Portugal taking a huge lead over Castile in colonization and expansion (taking Granada and North Africa). Eventually, Castile revolted with the help of France and Portugal, and Aragon almost died.
Eastern Europe is pretty unique too:
Poland chose a local noble and eventually fell in a PU under Sweden. Lithuania + Poland were repeatedly beating Muscovy, but once Lithuania lost Poland, they started losing ground to Muscovy again, but both countries are a complete failure, keep revolting and bankrupting, and Sunni AI Perm actually just won a war against Muscovy.
The HRE is actually the less random area, even if it is entirely Protestant/Reformed, with Wurtemberg as the Emperor since the League Wars.
Asia isn't bad either by the way:
Stable AI Uzbek (but this is VH so this probably helps them), and Manchu and Japan fighting over control of Korea. Ming started exploding twice but somehow came back both times. This is the third time they're in a disaster, this time with Nomad frontier because of Manchu. Usually they either collapse early or remain stable, here they passed all reforms but keep revolting and have low mandate more often than not. I'm hoping for AI Qing, this looks very possible.
Edit: Wait, I had not even looked at Africa. What is that Africa? That has to be the strangest one actually.
Kilwa and Ethiopia gone. Blobbing Kaffa, Mombasa, Sofala, and Antemoro (the weakest of all the tags on Madagascar iirc).
Edit:
Did not notice Nogai switched to Rurikovich dynasty (no idea how) until I got a Rurikovich consort from them.