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.
      [1913 Webster]

   2. To divide into separate parts or subdivision.
      [1913 Webster]

   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.
      [1913 Webster]

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.
   [1913 Webster]

         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.
   [1913 Webster]

         The sciences, with their numerous branchings. --L.
                                                  Watts.
   [1913 Webster]

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]

Moby Thesaurus II by Grady Ward, 1.0:

67 Moby Thesaurus words for "branching":
   V-shaped, Y-shaped, arboreal, arborescence, arborescent,
   arboriform, arborization, bifidity, biforked, biforking, bifurcate,
   bifurcated, bifurcation, bipartition, bisected, bisection, bowery,
   branched, branching off, branchlike, branchy, by two, cleft,
   cloven, crotched, cutting in two, dendriform, dendritic,
   dichotomous, dichotomy, dimidiate, dimidiation, divarication,
   divided, division, foliaged, foliate, foliated, foliose, forked,
   forking, forklike, furcate, furcation, halved, halving, in half,
   leafy, leaved, leavy, pronged, ramate, ramification, ramified,
   ramose, ramous, riven, split, subdivision, tree-shaped, treelike,
   treelikeness, tridentlike, trifurcate, trifurcated, trifurcation,
   twiggy