  We revisit $F_\pi(Q^2)$ and $F_{P\gamma}(Q^2)$, $P=\pi,\eta,\eta'$, making
use of the local-duality (LD) version of QCD sum rules. We give arguments, that
the LD sum rule provides reliable predictions for these form factors at $Q^2
\ge 5-6$ GeV$^2$, the accuracy of the method increasing with $Q^2$ in this
region. For the pion elastic form factor, the well-measured data at small $Q^2$
give a hint that the LD limit may be reached already at relatively low values
of momentum transfers, $Q^2\approx 4-8$ GeV$^2$; we therefore conclude that
large deviations from LD in the region $Q^2=20-50$ GeV$^2$ seem very unlikely.
The data on the ($\eta,\eta')\to\gamma\gamma^*$ form factors meet the
expectations from the LD model. However, the {\sc BaBar} results for the
$\pi^0\to\gamma\gamma^*$ form factor imply a violation of LD growing with $Q^2$
even at $Q^2\approx 40$ GeV$^2$, at odds with the $\eta,\eta'$ case and with
the general properties expected for the LD sum rule.
