  Information on the Sivers distribution and the Collins fragmentation
functions and their transverse momentum dependence is mainly based on fitting
single spin asymmetry data from semi-inclusive deep inelastic scattering
(SIDIS). Independent information, respectively on the Sivers distribution and
the Collins fragmentation, can be obtained from Drell-Yan and $e^+e^-$
annihilation processes. In the SIDIS case, the transverse momentum of the final
observed hadron, which is the quantity measured, is generated both by the
average transverse momentum in the distribution and in the fragmentation
functions. As a consequence, these are strongly correlated and a separate
extraction is made difficult. In this paper we investigate, in a simple
kinematical Gaussian configuration, this correlation, its role on the
transverse single spin asymmetries in SIDIS and the consequences for
predictions of the Sivers asymmetry in Drell-Yan processes and for the Collins
asymmetry in $e^+e^-$ annihilation. We find that, in some cases, these effects
can be relevant and must be carefully taken into account.
