[en] We present theoretical predictions for selected differential cross sections for the process pp → $t\stackrel{¯<!--\; ??\; -->}{t}$B at the LHC, where B can be a Higgs (H), a Z or a W boson. The predictions are calculated in the direct QCD framework up to the next-to-next-leading logarithmi accuracy and matched to the complete NLO results including QCD and electroweak effects. Additionally, results for the total cross sections are provided. The calculations deliver a significant improvement of the theoretical predictions, especially for the $t\stackrel{¯<!--\; ??\; -->}{t}$H and the $t\stackrel{¯<!--\; ??\; -->}{t}$Z production. In these cases, predictions for both the total and differential cross sections are remarkably stable with respect to the central scale choice and carry a substantially reduced scale uncertainty in comparison with the complete NLO predictions.