Zaddik

Some Rabbis without any jewish roots; all of them are converts to judaism (gerrim):

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Rabbi Dr. Asher Wade (Chassidut Gur/Ger)

http://www.youtube.com/watch?v=nszEJE70dvk

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Rabbi Natan Gamedze (African black haredi litvish Rabbi)

http://www.youtube.com/watch?v=7qtid87l4xY

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Rabbi Yaakov Ephraim Parisi (Chassidut Chabad-Lubavitch)

http://www.chabad.org/multimedia/media_cdo/aid/1416870/jewish/A-Pastors-Journey-to-Judaism.htm

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Rabbi Moshe Hattori (japanese convert to orthodox Judaism)

http://www.youtube.com/watch?v=RPLsmwEbEjk

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Rabbi Binyamin Klugger (french convert and Chabad-Lubavitch Rabbi)

Rabbi YY Rubinstein

So gerrim CAN become rabbis!