Diverge, subdivide, as in It's the house on the left, just after the road branches off, or English and Dutch branched off from an older parent language, West Germanic. This term alludes to a tree's growth pattern, in which branches grow in separate directions from the main trunk. [Second half of 1800s] Also see branch out.
Examples from the Web for branch off
Branch-off connectors such are shown in Figure 206 are often used to tap off lights from the main cable.Motion Picture Operation, Stage Electrics and Illusions|Henry C. Horstmann