  We consider QCD radiative corrections to the associated production of a
heavy-quark pair ($Q{\bar Q}$) with a generic colourless system $F$ at hadron
colliders. We discuss the resummation formalism for the production of the
$Q{\bar Q}F$ system at small values of its total transverse momentum $q_T$. The
perturbative expansion of the resummation formula leads to the explicit
ingredients that can be used to apply the $q_T$ subtraction formalism to
fixed-order calculations for this class of processes. We use the $q_T$
subtraction formalism to perform a fully differential perturbative computation
for the production of a top-antitop quark pair and a Higgs boson. At
next-to-leading order we compare our results with those obtained with
established subtraction methods and we find complete agreement. We present, for
the first time, the results for the flavour off-diagonal partonic channels at
the next-to-next-to-leading order.
