  We study the pion-photon transition form factor (TFF)
$F^{\gamma*\gamma\pi^0}(Q^2)$ using a state-of-the art implementation of light
cone sum rules (LCSRs) within fixed-order QCD perturbation theory. The spectral
density in the dispersion relation includes all currently known radiative
corrections up to the next-to-next-to-leading-order (NNLO) and all twist
contributions up to order six. Predictions for the TFF are obtained for various
pion distribution amplitudes (DAs) of twist two, including two-loop evolution
which accounts for heavy-quark mass thresholds. The influence of the main
theoretical uncertainties is quantified in order to enable a more realistic
comparison with the data. The characteristics of various pion DAs are analyzed
in terms of the conformal coefficients $a_2$ and $a_4$ in comparison with the
$1\sigma$ and $2\sigma$ error regions of the data and the most recent lattice
constraints on $a_2$ with NLO and NNLO accuracy. Our results provide more
stringent bounds on the variation of the pion DA and illuminate the
corresponding asymptotic behavior of the calculated TFF.
