The γ* → γf2(1270) and γ* → γa2(1320) transition form factors are considered up to high energies, along with the cross sections for the respective processes e+e− → γ* → f2γ and e+e− → γ* → a2γ. It is shown that QCD asymptotic behavior of the amplitudes for the reactions e+e− → γ* → f2γ and e+e− → γ* → a2γ can be reached after the compensation of the contributions of the ρ(770) and ω(782) mesons with the contributions of their radial excitations. The ratio σ(e+e− → γ* → f2γ)/σ(e+e− → γ* → a2γ) ≈ 25/9, obtained on the basis of the two-quark model of a2 and f2 and within QCD, is used to determine σ(e+e− → γ* → a2γ) at high energies. Recent data from the Belle detector on the γ*(Q2)γ → f2 transition over the region extending up to Q2 = 30 GeV2 are taken into account. A substantial improvement of experimental accuracies is required for a detailed comparison of our predictions with experimental data at high energies. A recent measurement of the e+e− → f2γ → π+π−γ cross section at 10.58 GeV with the BaBar detector gives grounds to hope for this.