  We consider parton showers based on radiation from QCD dipoles or `antennae'.
These showers are built from 2->3 parton splitting processes. The question then
arises of what functions replace the Altarelli-Parisi splitting functions in
this approach. We give a detailed answer to this question, applicable to
antenna showers in which partons carry definite helicity, and to both initial-
and final-state emissions.
