  We study the exclusive production of scalar $S = 0^{++}$ and tensor $T =
2^{++}$ mesons through single-photon annihilation $e^+ e^- \to \gamma^* \to
\gamma S(T)$. Using QCD compositeness of the involved hadrons considered as
quark-antiquark systems, the prediction for the scaling of the differential
cross sections of these processes is $d\sigma/dt \sim 1/s^3$ at large $s$. We
further derive the scaling of the $\gamma^\ast \to \gamma S$ and $\gamma^\ast
\to \gamma T$ transition form factors: $F_{\gamma^\ast\gamma S}(s) \sim 1/s$
and $F_{\gamma^\ast\gamma T}(s) \sim 1/s^2$. Results for the respective cross
sections of the scalar and tensor meson production are presented. Note, when
scalar and tensor mesons are considered as tetraquark systems of two tightly
bound color diquarks, corresponding to them transition form factors and
differential cross sections have the same falloffs as in case of
quark-antiquark picture. For other tetraquark or two-hadron molecules
configurations the transition form factors $F_{\gamma^\ast\gamma S(T)}(s)$ and
the differential cross section $d\sigma/dt$ have additional $1/s$ and $1/s^2$
falloffs, respectively.
