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We present the results of a systematic analysis of a group of Type II plateau supernovae that span a large range in luminosities, from faint objects like SN 1997D and 1999br to very luminous events like SN 1992am. The physical properties of the supernovae appear to be related to the plateau luminosity or the expansion velocity. The simultaneous analysis of the observed light curves, line velocities and continuum temperatures leads us to robust estimates of the physical parameters of the ejected envelope. We find strong correlations among several parameters. The implications of these results regarding the nature of the progenitor, the central remnant and the Ni yield are also addressed.