  We consider the decay of a polarized top quark into a polarized W-boson plus
a bottom quark, followed by the decay of the W-boson into a pair of leptons or
quarks. The polar angle distribution of the top spin relative to the W-momentum
and the polar angle distribution of the lepton (or quark) in the W-rest frame
is governed by three polarized and three unpolarized rate functions which are
related to the double density matrix elements of the decay $t \to W^+ + b$. We
obtain analytical expressions for the $O(\alpha_s)$ radiative corrections to
the three polarized and three unpolarized rate functions. We also provide a
comprehensive discussion of the dependence of the longitudinal, transverse and
normal polarization of the top quarks produced at $e^+e^-$-colliders on beam
polarization parameters.
