  The large-$Q^2$ behavior of $\eta_c$-$\gamma$ and $\eta_b$-$\gamma$
transition form factors, $F_{\eta_c\gamma}(Q^2)$ and $F_{\eta_b\gamma}(Q^2)$
are analyzed in the framework of light-cone perturbative QCD with the heavy
quark ($c$ and $b$) mass effect, the parton's transverse momentum dependence
and the higher helicity components in the light-cone wave function are
respected. It is pointed out that the quark mass effect brings significant
modifications to the asymptotic predictions of the transition form factors in a
rather broad energy region, and this modification is much severer for
$F_{\eta_b\gamma}(Q^2)$ than that for $F_{\eta_c\gamma}(Q^2)$ due to the
$b$-quark being heavier than the $c$-quark. The parton's transverse momentum
and the higher helicity components are another two factors which decrease the
perturbative predictions. For the transition form factor
$F_{\eta_c\gamma}(Q^2)$, they bring sizable corrections in the present
experimentally accessible energy region ($Q^2 \leq 10 GeV^2$). For the
transition form factor $F_{\eta_b\gamma}(Q^2)$, the corrections coming from
these two factors are negligible since the $b$-quark mass is much larger than
the parton's average transverse momentum. The coming $e^+ e^-$ collider (LEP2)
will provide the opportunity to examine these theoretical predictions.
