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As many advertising systems open popups, I was wondering what if from my site A I make (randomly, I mean not every time) a window.open(B)?
Could one of the sites get banned?
Indirectly, yes. Users will spend less time on your website because you have annoying popup advertising. They will return to the search page with the same query looking for another source, and that's bad for your search position.
No absolutely non of these sites will get banned or penalized.
Required, but never shown