  Some estimates for the transverse Single Spin Asymmetry, A_N, in the
inclusive processes l p(transv. pol.) --> h X, given in a previous paper, are
expanded and compared with new experimental data. The predictions are based on
the Sivers distributions and the Collins fragmentation functions which fit the
azimuthal asymmetries measured in Semi-Inclusive Deep Inelastic Scattering
(SIDIS) processes (l p(transv. pol.) --> l' h X). The factorisation in terms of
Transverse Momentum Dependent distribution and fragmentation functions (TMD
factorisation) -- i.e., the theoretical framework in which SIDIS azimuthal
asymmetries are analysed -- is assumed to hold also for the inclusive process l
p --> h X at large P_T. The values of A_N thus obtained agree in sign and shape
with the data. Some predictions are given for future experiments.
