  We present an updated study of transverse single-spin asymmetries for the
inclusive large-$P_T$ processes $\ell \, p^\uparrow \to h\, X$ and $\ell\,
p^\uparrow \to {\rm jet}\,X$, within a transverse momentum-dependent approach,
including the contribution of quasireal (Weizs\"acker-Williams) photons. In the
spirit of a unified transverse momentum-dependent scheme, predictions are
obtained adopting the Sivers and transversity distributions and the Collins
fragmentation functions as extracted from fits to the azimuthal asymmetries
measured in semi-inclusive deep inelastic scattering and $e^+e^-$ annihilation
processes. The description of the available data is extremely good, showing a
clear general improvement with respect to the previous leading-order analysis.
Predictions for unpolarized cross sections and single-spin asymmetries for
ongoing and future experiments are also given.
