  The studies of the associated production processes of a top-quark pair with a
colour-singlet boson, e.g. Higgs, W or Z, are among the highest priorities of
the LHC programme. Correspondingly, improvements in precision of theoretical
predictions for these processes are of central importance. In this talk, we
review our latest results on resummation of soft gluon corrections. The
resummation is carried out using the direct QCD Mellin space technique in
three-particle invariant mass kinematics. We discuss the impact of the soft
gluon corrections on predictions for total cross sections and differential
distributions.
