We present a generalization of the multiphase chemical evolution model applied to a wide set of theoretical galaxies with different masses and evolutionary rates. This generalized set of models has been computed using the so-called Universal Rotation Curve from Persic et al. (1996MNRAS.281...27P) to calculate the radial mass distribution of 44 theoretical protogalaxies. This distribution is a fundamental input which, besides its own effect on the galaxy evolution, defines the characteristic collapse time-scale or gas infall rate onto the disc. We have adopted 10 sets of values, between 0 and 1, for the molecular cloud and star formation efficiencies, as corresponding to their probability nature, for each one of the radial distributions of total mass. Thus, we have constructed a bi-parametric grid of models, depending on those efficiency sets and on the rotation velocity, whose results are valid in principle for any spiral or irregular galaxy. The model results provide the time evolution of different regions of the disc and the halo along galactocentric distance, measured by the gas (atomic and molecular) and stellar masses, the star formation rate and chemical abundances of 14 elements, for a total of 440 models. This grid may be used to estimate the evolution of a given galaxy for which only present time information, such as radial distributions of elemental abundances, gas densities and/or star formation, which are the usual observational constraints of chemical evolution models, is available.