  The process $e^{+}e^{-}\rightarrow\gamma^{*}\rightarrow \pi^{0}\gamma$ was
considered using time-like pion transition form factor, obtained in the
approach of the Anomaly Sum Rules(ASR). The total cross section and angular
distribution of the process was calculated. As the result of the comparison
with the data it was shown that ASR approach provides their good description in
the regions far from the pole. Also there was proposed a method allowing to
give reasonable description of data in the region of pole within the ASR
approach. The strong restrictions for the parameters of the modified ASR
approach were obtained.
