  We compute the differential and total rate of the semileptonic decay of
polarized top-quarks $t\to \ell \nu_\ell + b{\rm jet} + {\rm jet}$ at
next-to-leading order (NLO) in the QCD coupling with an off-shell intermediate
$W$ boson. We present several normalized distributions, in particular those
that reflect the $t$-spin analyzing powers of the lepton, the b-jet and the
$W^+$ boson at LO and NLO QCD.
