  We discuss the evolution of the eight leading twist transverse momentum
dependent parton distribution functions, which turns out to be universal and
spin independent. By using the highest order perturbatively calculable
ingredients at our disposal, we perform the resummation of the large logarithms
that appear in the evolution kernel of transverse momentum distributions up to
next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the
kernel with highly reduced model dependence. Our results can also be obtained
using the standard CSS approach when a particular choice of the $b^*$
prescription is used. In this sense, and while restricted to the perturbative
domain of applicability, we consider our results as a "prediction" of the
correct value of $b_{\rm max}$ which is very close to $1.5 {\rm GeV}^{-1}$. We
explore under which kinematical conditions the effects of the non-perturbative
region are negligible, and hence the evolution of transverse momentum
distributions can be applied in a model independent way. The application of the
kernel is illustrated by considering the unpolarized transverse momentum
dependent parton distribution function and the Sivers function.
