  The associated production of charged Higgs bosons and top quarks at hadron
colliders is an important discovery channel to establish the existence of a
non-minimal Higgs sector. Here, we present details of a next-to-leading order
(NLO) calculation of this process using the Catani-Seymour dipole formalism and
describe its implementation in POWHEG, which allows to match NLO calculations
to parton showers. Numerical predictions are presented using the PYTHIA parton
shower and are compared to those obtained previously at fixed order, to a
leading order calculation matched to the PYTHIA parton shower, and to a
different NLO calculation matched to the HERWIG parton shower with MC@NLO. We
also present numerical predictions and theoretical uncertainties for various
Two Higgs Doublet Models at the Tevatron and LHC.
