  The behavior of the transition pion form factor for processes \gamma^*\gamma
-> \pi^0 and \gamma^* \gamma^* -> \pi^0 at large values of space-like photon
momenta is estimated within the nonlocal covariant quark-pion model. It is
shown that, in general, the coefficient of the leading asymptotic term depends
dynamically on the ratio of the constituent quark mass and the average
virtuality of quarks in the vacuum and kinematically on the ratio of photon
virtualities. The kinematic dependence of the transition form factor allows us
to obtain the relation between the pion light-cone distribution amplitude and
the quark-pion vertex function. The dynamic dependence indicates that the
transition form factor \gamma^* \gamma -> \pi^0 at high momentum transfers is
very sensitive to the nonlocality size of nonperturbative fluctuations in the
QCD vacuum.
