We measure radial gradients of the Mg2 index in 15 E-E/S0 and 14 S0 galaxies. Our homogeneous data set covers a large range of internal stellar velocity dispersions (2.0<logsigma<2.5) and Mg2 gradients (dMg2/dlogr/re* up to -0.14mag/dex). We find for the first time, a noticeable lower boundary in the relation between Mg2 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 which 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 with previous works which found a correlation between dMg2/dlogr/re* and sigma confined to the low mass galaxies, suggesting that only galaxies below some limiting sigma were formed by collapse whereas the massive ones by mergers. We show observational evidence that a hybrid scenario could arise also among massive galaxies. Finally, we estimated d[Z/H] from Mg2 and Hbeta measurements and single stellar population models. The conclusions remain the same, indicating that the results cannot be ascribed to age effects on Mg2.