  Using the model of Nambu and Jona-Lasinio to provide a microscopic
description of both the structure of the nucleon and of the quark to hadron
elementary fragmentation functions, we investigate the transverse momentum
dependence of the unpolarized quark distributions in the nucleon and of the
quark to pion and kaon fragmentation functions. The transverse momentum
dependence of the fragmentation functions is determined within a Monte Carlo
framework, with the notable result that the average $P_\perp^2$ of the produced
kaons is significantly larger than that of the pions. We also find that
$<P_\perp^2>$ has a sizable $z$ dependence, in contrast with the naive Gaussian
ansatz for the fragmentation functions. Diquark correlations in the nucleon
give rise to a non-trivial flavor dependence in the unpolarized transverse
momentum dependent quark distribution functions. The $<k_T^2>$ of the quarks in
the nucleon are also found to have a sizable $x$ dependence. Finally, these
results are used as input to a Monte Carlo event generator for semi-inclusive
deep inelastic scattering (SIDIS), which is used to determine the average
transverse momentum squared of the produced hadrons measured in SIDIS, namely
$<P_T^2>$. Again we find that the average $P_T^2$ of the produced kaons in
SIDIS is significantly larger than that of the pions and in each case $\la
P_T^2 \ra$ has a sizable $z$ dependence.
