Pion transition form factor: interplay of hard and soft limits

The behaviour of the pion transition form factor for the process ${\gamma }^{\star }\gamma \to {\pi }^0$ and ${\gamma }^{\star }{\gamma }^{\star }\to {\pi }^0$ at space-like values of photon momenta is estimated within the nonlocal covariant quark-meson model. The nonlocal contributions are important to install the axial anomaly at zero photon virtualities and give the contributions to the twist-4 power correction to the form factor at large virtualities. The leading and next-to-leading order power asymptotics of the form factor and the relation between the light-cone pion distribution amplitudes and the dynamically generated quark mass function are found.