  We show that in fully-self-consistent treatments of the pion; namely, its
static properties and elastic and transition form factors, the asymptotic limit
of the product Q^2 G_{\gamma * \gamma \pi ^0}(Q^2), determined a priori by the
interaction employed, is not exceeded at any finite value of spacelike momentum
transfer. Furthermore, in such a treatment of a vector-vector
contact-interaction one obtains a \gamma * \gamma -> \pi ^0 transition form
factor that disagrees markedly with all available data. We explain that the
contact interaction produces a pion distribution amplitude which is flat and
nonvanishing at the endpoints. This amplitude characterises a pointlike pion
bound-state. Such a state has the hardest possible form factors; i.e., form
factors which become constant at large momentum transfers and hence are in
striking disagreement with completed experiments. On the other hand,
interactions with QCD-like behaviour produce soft pions, a valence-quark
distribution amplitude that vanishes as ~(1-x)^2 for x~1, and results that
agree with the bulk of existing data. Our analysis supports a view that the
large-Q^2 data obtained by the BaBar Collaboration is not an accurate measure
of the \gamma * \gamma -> \pi ^0 form factor.
