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 950 GeV. Limits are quoted at 95% CL and are indicated for the data (solid 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].