We compute the complete next-to-leading order SUSY-QCD corrections for the
associated production of a charged Higgs boson with a top quark via
bottom-gluon fusion. We investigate the applicability of the bottom parton
description in detail. The higher order corrections can be split into real and
virtual corrections for a general two Higgs doublet model and into additional
massive supersymmetric loop contributions. We find that the perturbative
behavior is well under control. The supersymmetric contributions consist of the
universal bottom Yukawa coupling corrections and non-factorizable diagrams.
Over most of the relevant supersymmetric parameter space the Yukawa coupling
corrections are sizeable, while the remaining supersymmetric loop contributions
are negligible.Comment: 18 pages, v2: some discussions added, v3: published versio