  Within a perturbative approach to Quantum Chromodynamics (QCD), we show how
to extend ordinary DGLAP longitudinal evolution equations to include the
radiative transverse momentum generated in the collinear branching regime.
Considering Semi-inclusive Deep Inelastic Scattering as a reference process, we
perform such a generalization both in the current and in the target
fragmentation region. These distributions are then used to predict
semi-inclusive Deep Inelastic Scattering cross-sections onto the whole phase
space of the detected hadron.
