who is the closest person today to being the successor of the Lubavitch Rebbi?
i.e. who is the biggest (greatest scholar) Chabad Rabbi to ask questions to about Chabad issues.
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Rabbis Moshe Kotlarsky and Rabbi Yehuda Krinsky currently head the Lubavitch institutions. See more here, including a discussion of their succession plans.
As for which Chabad Rabbi is known as the greatest scholar today, I don't know but the one who comes to my mind immediately would be Rabbi Adin Steinzaltz, whose name had been briefly floated by some outsiders as a great choice for an eighth Lubavitcher rebbe.
Reb Yoel Kahn is "the" giant master in chassidus