We measure radial gradients of the Mg sub(2) index in 15 E-E/S0 and 14 SO galaxies. Our homogeneous data set covers a large range of internal stellar velocity dispersions (2.0 < log sigma < 2.5) and Mg sub(2) gradients Delta Mg sub(2)/ Delta log (r/r* sub(e)) up to -0.14 mag dex super(-1). We find for the first time a noticeable lower boundary in the relation between Mg sub(2) gradient and sigma along the full range of sigma , which may be populated by galaxies predominantly formed by monolithic collapse. At high sigma , galaxies showing flatter gradients could represent objects that suffered either important merging episodes or later gas accretion. These processes contribute to the flattening of the metallicity gradients, and their increasing importance could define the distribution of the objects above the boundary expected by the "classical" monolithic process. This result is in marked contrast to previous works, which found a correlation between Delta Mg sub(2)/ Delta log (r/r* sub(e)) and sigma confined to the low-mass galaxies, suggesting that only galaxies below some limiting sigma were formed by collapse, whereas the massive ones were formed by mergers. We show observational evidence that a hybrid scenario could also arise among massive galaxies. Finally, we estimate Delta Z/H from Mg sub(2) and H beta measurements and single stellar population models. The conclusions remain the same, indicating that the results cannot be ascribed to age effects on Mg sub(2).