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We revisit $F_\pi(Q^2)$ and $F_{P\gamma}(Q^2)$, $P=\pi,\eta,\eta'$, makinguse of the local-duality (LD) version of QCD sum rules. We give arguments, thatthe 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 thisregion. 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 valuesof momentum transfers, $Q^2\approx 4-8$ GeV$^2$; we therefore conclude thatlarge 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 theexpectations 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 withthe general properties expected for the LD sum rule.

Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules