Regions of the [m<sub>A</sub> , tan&beta; ] plane excluded in the hMSSM via direct searches for heavy Higgs bosons and fits to the measured rates of observed Higgs boson production and decays, with m<sub>A</sub> in the range from 200 GeV to 2 TeV. Limits are quoted at 95% CL and are indicated for the data (solid lines) and the expectation for the SM Higgs sector (dashed lines). The light shaded or hatched regions indicate the observed exclusions. Unless otherwise specified, only gluon--gluon fusion (gg) is considered for the production mode. The cross-sections for the Higgs boson production in the hMSSM [15,16,17] are calculated using up to NNLO QCD corrections for gluon--gluon fusion and b-associated production in the five-flavour scheme as implemented in Sushi [25,26,27,28,29]. For b-associated production a cross-section in the four-flavour scheme is calculated as described in Refs. [30,31] and the results are combined with the five-flavour scheme calculation following Ref. [32]. The Higgs boson widths and branching ratios have been calculated using HDECAY [33]. For the tanti-tH/A, H/A&rarr; tanti-t search, the heavy Higgs boson is produced in association with tanti-t; the cross section for this process is calculated using MadGraph5<sub>A</sub>MC@NLO [34] and the procedure described in Ref. [19]. The charged Higgs boson production in association with top in H<sup>&</sup>plusmn;&rarr; tb search results follows Ref. [19]. The procedure for the calculation of the cross-sections and the branching ratios follows Ref. [35]. Discussion of the approximations used in the hMSSM and their validity can be found in Ref. [18].