WordNet sense 1 (a part of a forked or branching shape):

leg, ramification

WordNet sense 2 (a natural consequence of development):

offset, offshoot, outgrowth

WordNet sense 3 (an administrative division of some larger or more complex organization):

arm, subdivision

WordNet sense 4 (any projection that is thought to resemble a human arm):

limb

WordNet sense 5 (grow and send out branches or branch-like structures):

ramify

WordNet sense 6 (divide into two or more branches so as to form a fork):

fork, separate, furcate, separate