  We consider top quark pair production in association with a hard jet through
next-to-leading order in perturbative QCD. Top quark decays are treated in the
narrow width approximation and spin correlations are retained throughout the
computation. We include hard jet radiation by top quark decay products and
explore their importance for basic kinematic distributions at the Tevatron and
the LHC. Our results suggest that QCD corrections and jet radiation in decays
can lead to significant changes in shapes of basic distributions and,
therefore, need to be included for the description of ttbar+jet production. We
compare the shape of the transverse momentum distribution of a top quark pair
recently measured by the D0 collaboration with the result of our computation
and find reasonable agreement.
