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.
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            To branch out into a long disputation. --Spectator.
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The Collaborative International Dictionary of English v.0.48:

Branching \Branch"ing\, a.
   Furnished with branches; shooting our branches; extending in
   a branch or branches.
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         Shaded with branching palm.              --Milton.
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The Collaborative International Dictionary of English v.0.48:

Branching \Branch"ing\, n.
   The act or state of separation into branches; division into
   branches; a division or branch.
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         The sciences, with their numerous branchings. --L.
                                                  Watts.
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WordNet (r) 3.0 (2006):

branching
    adj 1: having branches [syn: branched, branching, ramose,
           ramous, ramate]
    2: resembling the branches of a tree
    n 1: the act of branching out or dividing into branches [syn:
         branching, ramification, fork, forking]