  We study photon--meson transition form factors $\gamma^*(Q^2)\gamma \to
\pi^0,\eta,\eta'$ at low and moderately high virtualities $Q^2$ of one of the
photons, the second photon being real. For the description of the form factor
at low $Q^2$, a nontrivial quark--antiquark $(q\bar q)$ structure of the photon
in the soft region is assumed, i.e. the photon is treated much like an ordinary
vector meson. At large $Q^2$, along with a perturbative tail of the soft wave
function, as it is for a hadron, the photon wave function contains also a
standard QED point-like $q\bar q$ component. The latter provides the $1/Q^2$
behavior of the transition form factor at large $Q^2$ in accordance with
perturbative QCD. Using the experimental results on $\gamma\pi^0$ form factor,
we reconstruct the soft photon wave function which is found to have the
structure similar to pion's, which has been formerly determined from a study of
the elastic pion form factor. Assuming the universality of the ground--state
pseudoscalar meson wave functions we calculate the transition form factors
$\gamma\eta$, $\gamma\eta'$ and partial widths $\eta\to\gamma\gamma$,
$\eta'\to\gamma\gamma$, in a perfect agreement with data.
