In this presentation I will report on the state-of-the-art NLO QCD computation for the pp → tt + V process in the di-lepton channel at the LHC with sqrt(s) = 13 TeV. I will describe calculations with off-shell top quarks, double-, single- as well as non-resonant top-quark contributions along with all interference effects, which are consistently incorporated at the matrix element level. I will present results in the form of fiducial integrated and differential cross sections. The impact of top quark modelling will be scrutinised by an explicit comparison with the results in the narrow-width approximation. Finally, a comparison with the ATLAS results will be presented.