Branching rhymes with:
ranching, ranching, stanching, bunching, clinching, crunching, drenching, entrenching, flinching, inching, launching, lunching, lynching, munching, pinching, punching, quenching, ranching, retrenching, stanching, unflinching, wrenching
Branching sounds like:
brainwashing, branson's, bringing, brinkmann's