  The $\gamma^* \pi^0 \rightarrow \gamma$ form factor, including the extension
off the pion mass-shell, is obtained from a generalized impulse approximation
within a QCD-based model field theory known to provide an excellent description
of the pion charge form factor. This approach implements dressing of the vertex
functions and propagators consistent with dynamical chiral symmetry breaking,
gauge invariance, quark confinement and perturbative QCD. Soft nonperturbative
behavior, dictated by the axial anomaly, is found to evolve to the perturbative
QCD limit only for \mbox{$Q^2 \geq 20~{\rm GeV}^2$}.
