to branch off

from The Collaborative International Dictionary of English v.0.48
Branch \Branch\, v. i. [imp. & p. p. {Branched}; p. pr. & vb. n.
   {Branching}.]
   1. To shoot or spread in branches; to separate into branches;
      to ramify.
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   2. To divide into separate parts or subdivision.
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   {To branch off}, to form a branch or a separate part; to
      diverge.

   {To branch out}, to speak diffusively; to extend one's
      discourse to other topics than the main one; also, to
      enlarge the scope of one's business, etc.
      [1913 Webster]

            To branch out into a long disputation. --Spectator.
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