Hadronic Higgs production through NLO [Formula: see text]  PS in the SM, the 2HDM and the MSSM

The next-to-leading order (NLO) cross section of the gluon fusion process is matched to parton showers in the MC@NLO approach. We work in the framework of MadGraph5_aMC@NLO and document the inclusion of the full quark-mass dependence in the Standard Model (SM) as well as the state-of-the-art squark and gluino effects within the Minimal Supersymmetric SM embodied in the program SusHi. The combination of the two programs is realized by a script which is publicly available and whose usage is detailed. We discuss the input cards and the relevant parameter switches. One of our focuses is on the shower scale which is specifically important for gluon-induced Higgs production, particularly in models with enhanced Higgs-bottom Yukawa coupling.