  Results for the two real parton differential distributions needed for
implementing a next-to-leading order (NLO) parton shower Monte Carlo are
presented. They are also integrated over the phase space in order to provide
solid numerical control of the MC codes and for the discussion of the
differences between the standard $\bar{MS}$ factorization and Monte Carlo
implementation at the level of inclusive NLO evolution kernels. Presented
results cover the class of non-singlet diagrams entering into NLO kernels. The
classic work of Curci-Furmanski-Pertonzio was used as a guide in the
calculations.
