  In the TMD approach, the average transverse momentum of the unpolarised TMD
PDFs and FFs is crucial not only to reproduce unpolarised cross sections and
hadron multiplicities, but also for the understanding of azimuthal and spin
asymmetries. Information on these transverse momenta is nowadays obtained
mainly by fitting multiplicities data for SIDIS, where the intrinsic motion in
the initial parton distributions and in the hadronisation process are strongly
correlated and difficult to estimate separately without ambiguities. In this
contribution we discuss the consequences of this correlation effects on the
predictions for the Sivers and Collins asymmetries measured in SIDIS and
$e^+e^-$ annihilations, and under active investigation for Drell-Yan processes
at RHIC and at CERN by the COMPASS experiment. We show that these effects may
be relevant and can sensibly modify the size of the predicted asymmetries.
Therefore, they must be taken into careful account when investigating other
aspects of TMDs, like the evolution properties of the Sivers and Collins
functions and the expected process dependence of the Sivers function.
