So i have tried to ask this many times on ingame chat with no results...does the abdicate button in embassy appear only after starting to deactivate your treasury being already out of BP?

abdication
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Yes you need to deactivate (or remove) your treasury, not sure for king if you need 200 pop to change (for gov you do)
as you are talking BP I'm guessing you're on a new server) so no unions will have happened yet (once you Unite with another kingdom, you can no longer abdicate for the rest of the server)