  We calculate transverse momentum dependent quark splitting kernels $P_{gq}$
and $P_{qq}$ within $k_T$-factorization, completing earlier results which
concentrated on gluon splitting functions $P_{gg}$ and $P_{qg}$. The complete
set of splitting kernels is an essential requirement for the formulation of a
complete set of evolution equations for transverse momentum dependent parton
distribution functions and the development of corresponding parton shower
algorithms.
