  We investigate the form factors for pseudoscalar-meson-photon transitions by
means of dispersive QCD sum rules and demonstrate that most of the measurements
done so far (in particular, those by BaBar for $\eta,$ $\eta',$ and $\eta_c$
and those by Belle for $\pi^0$) are, on the one hand, compatible with each
other and with the saturation required by factorization theorems obtained from
perturbative QCD and, on the other hand, give a hint that saturation is
effective already at relatively low momentum transfers $Q^2;$ this hypothesis
is supported by experimental data for the charged-pion elastic form factor
available in the range $Q^2\approx2-4\;\{GeV}^2.$ The only exception are the
BaBar results for the $\pi^0\gamma$ transition form factor, which do not fit
into such picture. We point out that results expected from SHMS at JLab on the
pion elastic form factor in the region $Q^2\approx5-8\;\{GeV}^2$ will provide
the ultimate test of saturation and factorization and strongly impact our
general view of the form factors up to infinitely large $Q^2.$
