  The Dalitz distribution and the effective mass spectrum of the lepton pair
produced in the decay $\eta_c\to \gamma \ell^+ \ell^-$, as well as the
differential cross sections for the crossed channels $\gamma e^-\to \eta_c e^-
$ and $e^+ e^-\to \eta_c \gamma$, are calculated in terms of the sole
electromagnetic transition form factor for the vertex $\eta_c\to\gamma
\gamma^*$, where $\gamma^*$ is a virtual photon with a space-like (for $\gamma
e^- \to \eta_c e^- $) or a time-like (for $e^+ e^-\to \eta_c \gamma$ and
$\eta_c\to\gamma \ell^+\ell^-$) four-momentum. Explicit parametrisations of the
transition form factor are found in two different approaches, namely in Vector
Dominance Model and in a QCD-inspired consideration on the basis of the process
$c \bar{c}\to \gamma \ell^+ \ell^-$, with zero relative three-momentum of the
annihilating quarks.
