  We calculate the omega --> pi0 gamma* and phi --> pi0 gamma* electromagnetic
transition form factors based on dispersion theory, relying solely on a
previous dispersive analysis of the corresponding three-pion decays and the
pion vector form factor. We compare our findings to recent measurements of the
omega --> pi0 mu+ mu- decay spectrum by the NA60 collaboration, and strongly
encourage experimental investigation of the Okubo-Zweig-Iizuka-forbidden phi
--> pi0 l+ l- decays in order to understand the strong deviations from
vector-meson dominance found in these transition form factors.
