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We investigate the possibilities of studying new physics in various processesof t-quark production using kinematical distributions of the secondary leptoncoming from decay of t quarks. We show that the angular distributions of thesecondary lepton are insensitive to the anomalous tbW vertex and hence are pureprobes of new physics in a generic process of t-quark production. The energydistribution of the lepton is distinctly affected by anomalous tbW couplingsand can be used to analyze them independent of the production process of tquarks. The effects of t polarization on the distributions of the decay leptonare demonstrated for top-pair production process at a gamma-gamma collidermediated by a heavy Higgs boson.Comment: 15 pages, 7 figures, uses axodraw.sty (included), references added.  v3 to appear in Journal of High Energy Physics. Incorporates minor changes in  the discussion on radiative corrections which do not affect the results. Typo  in reference correcte

Lepton distribution as a probe of new physics in production and decay of thetquark and its polarization