Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi>η</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>η</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>transition form factors

We study the reactions ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}{\ensuremath{\eta}}^{(\ensuremath{'})}$ in the single-tag mode and measure the $\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}$ transition form factors in the momentum-transfer range from 4 to $40\text{ }\text{ }{\mathrm{GeV}}^{2}$. The analysis is based on $469\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected at PEP-II with the BABAR detector at ${e}^{+}{e}^{\ensuremath{-}}$ center-of-mass energies near 10.6 GeV.