  We present the QCD radiative corrections to the full off-shell $\rm
t\bar{t}W^+$ production, considering a final state with three charged leptons,
two b jets and missing energy. All interferences, off-shell effects and spin
correlations are included in the calculation. Beyond presenting integrated and
differential results for the full off-shell process, we compare them with those
obtained applying a double-pole approximation to the virtual corrections.
