  We complete the generalisation of the BCFW recursion relation to the
off-shell case, allowing for the computation of tree level scattering
amplitudes for full High Energy Factorisation (HEF), i.e. with both incoming
partons having a non-vanishing transverse momentum. We provide explicit results
for color-ordered amplitudes with two off-shell legs in massless QCD up to 4
point, continuing the program begun in two previous papers. For the 4-fermion
amplitudes, which are not BCFW-recursible, we perform a diagrammatic
computation, so as to offer a complete set of expressions. We explicitly show
and discuss some plots of the squared $2 \rightarrow 2$ matrix elements as
functions of the differences in rapidity and azimuthal angle of the final state
particles.
