  Transition form factors $F_{P\gamma^*\gamma^{(*)}}$ of pseudoscalar mesons
are studied within the framework of the domain model of confinement, chiral
symmetry breaking and hadronization. In this model, the QCD vacuum is described
by the statistical ensemble of domain wall networks which represents the almost
everywhere homogeneous Abelian (anti-)self-dual gluon field configurations.
Calculations of the form factors are performed consistently with mass spectra
of light, heavy-light and double-heavy mesons, their weak and strong decay
constants. Influence of the nonperturbative intermediate range gluon fields on
asymptotic behaviour of pion transition form factor is of particular interest,
as it can potentially lead to the growth of $Q^2F_{\pi\gamma^*\gamma}(Q^2)$. It
is found that $Q^2F_{\pi\gamma^*\gamma}(Q^2)$ approaches a constant value at
asymptotically large $Q^2$. However, this limit differs from the standard
factorization bound, though for pion form factor complies with Belle data more
likely than with BaBar ones. At the same time the generally accepted
factorization bound is shown to be satisfied for the case of the symmetric
kinematics, $Q^2F_{P\gamma^*\gamma^*}(Q^2)$. Peculiarities of description of
$\eta$, $\eta'$ and $\eta_c$ form factors within the model are discussed in
detail.
