We report on state-of-the-art theoretical predictions for $pp\to
t\bar{t}b\bar{b}$ including full off-shell effects in the di-lepton decay
channel at NLO QCD accuracy. We briefly discuss the impact of NLO QCD
corrections on differential distributions and also asses theoretical
uncertainties from scale and PDF dependence. Furthermore, we propose a simple
kinematic reconstruction in order to distinguish $b$ jets originating from
top-quark decays from arising from gluon splittings.