  Future high luminosity polarized deep--inelastic scattering experiments will
improve both the knowledge of the spin sub--structure of the nucleons and
contribute further to the precision determination of the strong coupling
constant, as well as, reveal currently yet unknown higher twist contributions
in the polarized sector. For all these tasks to be performed, it is necessary
to know the QCD leading twist scaling violations of the measured structure
functions. Here an important ingredient consists in the polarized singlet
anomalous dimensions and splitting functions in QCD. We recalculate these
quantities to three--loop order in the M--scheme by using the traditional
method of space--like off--shell massless operator matrix elements, being a
gauge--dependent framework. Here one obtains the anomalous dimensions without
referring to gravitational currents, needed when calculating them using the
forward Compton amplitude. We also calculate the non--singlet splitting
function $\Delta P_{\rm qq}^{(2), \rm s, NS}$ and compare the final results to
the literature, also including predictions for the region of small values of
Bjorken $x$.
