Closest thing I got to a definition of Gadol: the guy/s who make/s the decision re: who will speak at the siyum hashas and the seating arrangements on the dais.
on a serious note, if one were to translate lehavdil the three branches of government into Judaism, legislative powers are from Sinai, rabbonim (and/or cohanim) are the judiciary, but who is the executive? we don’t have a king anymore. I think it’s the involved laypersons. or at least it should be. separation of powers is a Jewish concept; chashmonaim were punished for not having it.