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In the TMD approach, the average transverse momentum of the unpolarised TMDPDFs and FFs is crucial not only to reproduce unpolarised cross sections andhadron multiplicities, but also for the understanding of azimuthal and spinasymmetries. Information on these transverse momenta is nowadays obtainedmainly by fitting multiplicities data for SIDIS, where the intrinsic motion inthe initial parton distributions and in the hadronisation process are stronglycorrelated and difficult to estimate separately without ambiguities. In thiscontribution we discuss the consequences of this correlation effects on thepredictions for the Sivers and Collins asymmetries measured in SIDIS and$e^+e^-$ annihilations, and under active investigation for Drell-Yan processesat RHIC and at CERN by the COMPASS experiment. We show that these effects maybe relevant and can sensibly modify the size of the predicted asymmetries.Therefore, they must be taken into careful account when investigating otheraspects of TMDs, like the evolution properties of the Sivers and Collinsfunctions and the expected process dependence of the Sivers function.

Unpolarised TMD PDFs and FFs and the role of transverse momentum dependence in azimuthal spin asymmetries