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We investigate the production of a heavy charged Higgs boson at hadroncolliders within the context of the MSSM. A detailed study is performed for allimportant production modes and basic background processes for thet\bar{t}b\bar{b} signature. In our analysis we include effects of initial andfinal state showering, hadronization, and principal detector effects. For thesignal production rate we include the leading SUSY quantum effects at high\tan\beta>~ mt/mb. Based on the obtained efficiencies for the signal andbackground we estimate the discovery and exclusion mass limits of the chargedHiggs boson at high values of \tan\beta. At the upgraded Tevatron the discoveryof a heavy charged Higgs boson (MH^+ >~ 200 GeV) is impossible for thetree-level cross-section values. However, if QCD and SUSY effects happen toreinforce mutually, there are indeed regions of the MSSM parameter space whichcould provide 3\sigma evidence and, at best, 5\sigma charged Higgs bosondiscovery at the Tevatron for masses M_H^+<~ 300 GeV and M_H^+<~ 250 GeV,respectively, even assuming squark and gluino masses in the (500-1000) GeVrange. On the other hand, at the LHC one can discover a H^+ as heavy as 1 TeVat the canonical confidence level of 5\sigma; or else exclude its existence at95% C.L. up to masses ~ 1.5 TeV. Again the presence of SUSY quantum effects canbe very important here as they may shift the LHC limits by a few hundred GeV.Comment: Latex2e, 44 pages, 15 figures, 6 tables, uses JHEP3.sty, axodraw.sty.  Comments added. Discussion on QCD factors clarified. Added discussion on  uncertainties. Change of presentation of Tables 4 and 5 and Fig.6. Results  and conclusions unchanged. Version accepted in JHE

Prospects for heavy supersymmetric charged Higgs boson searches at hadron colliders