  In this paper we study the production of a heavy charged Higgs boson in
association with heavy quarks at the LHC, in a type-II two-Higgs-doublet model.
We present for the first time fully-differential results obtained in the
four-flavour scheme at NLO accuracy, both at fixed order and including the
matching with parton showers. Relevant differential distributions are studied
for two values of the charged boson mass and a thorough comparison is performed
between predictions obtained in the four- and five-flavour schemes. We show
that the agreement between the two schemes is improved by NLO(+PS) corrections
for observables inclusive in the degrees of freedom of bottom quarks. We argue
that the four-flavour scheme leads to more reliable predictions, thanks to its
accurate description of the bottom-quark kinematics and its small dependence on
the Monte Carlos, which in turn is rather large in the five-flavour scheme. A
detailed set of recommendations for the simulation of this process in
experimental analyses at the LHC is provided.
