We report on our recent full off-shell pp→ttˉW+j+X calculation at the NLO level in QCD. Unstable resonant particles like the W±/Z vector bosons and top quarks are modelled with Breit-Wigner propagators. Furthermore double-, single- and non-resonant contributions as well as all their interference terms are consistently included at the matrix element level. We provide integrated and differential (fiducial) cross-section results and investigate the size of theoretical uncertainties as well as the impact of renormalization- and factorization scale settings on the theoretical predictions. Finally, we explore the effects of additional jet activity in ttˉW+ production and top-quark decays.