Various growths of the meson multiplicity n with large, total c.m. energy √ q 2in e + e − annihilation are related to corresponding behaviors of the single-particle-inclusive, photon- helicity-averaged structure function W . For values of the reduced energy variable x' = 2 ϵ/√ q 2 which belong to the central, region, two classes ofbehavior for W are discussed in the limit q 2→∞: (i) singular and (ii) non-singular. We emphasize a statistical model of class (ii) for which the growth n ∼ 2b −1(2p o − 1)ln q 2 is possible, where b = 3{ ζ(4)/ ζ(3)} and the exclusive form factor F(q 2)∼ (q 2) −po and p o > 1 2 . Amplitude W is specified in term of a Bose-Einstein distribution in the variable bζ, where ζ = x'/ x' . The total annihilation cross section σ ∼ σ pt/(ln q 2) 1 + δ , where σ pt = πα 2/3 q 2 and δ > 0, which leads to a convergent renormalization Z 3 hadron . A concrete model emerges for the excited hadronic constituents of the timelike photon (“partons”) in which a pointlike property of the constituents is characterized by particle spatial dimensions being measured in units of the small de Broglie wavelenth (in the c.m.s. of the e +e −-collision).