  For the spacelike momenta k of the virtual photon gamma^*, the pi^0(p)
gamma^*(k) gamma(k') transition form factor is considered in the coupled
Schwinger-Dyson and Bethe-Salpeter approach in conjunction with the generalized
impulse approximation using the dressed quark-photon-quark vertices of the
Ball-Chiu and Curtis-Pennington type. These form factors are compared with the
ones predicted by the vector meson dominance, operator product expansion, QCD
sum rules, and the perturbative QCD for the large spacelike transferred momenta
k. The most important qualitative feature of the asymptotic behavior, namely
the 1/k^2 dependence, is in our approach obtained in the model-independent way.
Again model-independently, our approach reproduces also the Adler-Bell-Jackiw
anomaly result for the limit of both photons being real. For the case of one
highly virtual photon, we find in the closed form the asymptotic expression
which can be easily generalized both to the case of other unflavored
pseudoscalar mesons P^0 = pi^0, eta_8, eta_0, eta_c, eta_b, and to the case of
arbitrary virtuality of the other photon. Implications thereof for certain
important theoretical and experimental applications are pointed out.
