Institut de Recherche sur les Lois Fondamentales de l'Univers

We briefly recall the main physical features of the parton distributions in the
quantum statistical picture of the nucleon. Some predictions from a next-to-leading
order QCD analysis are successfully compared to recent unpolarized and polarized
experimental results. We will discuss the extension to the transverse momentum
dependence of the parton distributions and its relevance for semi-inclusive deep inelastic
scattering. Finally, we will present some new positivity constraints for spin
observables and their implications for parton distributions.