c.1300, "limb of a tree" (also used of things analogous to it, especially geographic features), from O.Fr. branche, from L.L. branca "footprint," later "a claw, paw," of unknown origin, probably Gaulish. Meaning "local office of a business" is first recorded 1817, from earlier sense of "component part of a system" (1696). The verb meaning "to diverge from a central point" is first attested 1799.