We measure radial gradients of the Mg _ { 2 } index in 15 E - E / S 0 and 14 S 0 galaxies . Our homogeneous data set covers a large range of internal stellar velocity dispersions ( 2.0 < log \sigma < 2.5 ) and Mg _ { 2 } gradients ( \triangle Mg _ { 2 } / \triangle log r / r _ { e } ^ { * } Â up to -0.14 mag dex ^ { -1 } ) . We find for the first time , a noticeable lower boundary in the relation between Mg _ { 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 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 \triangle Mg _ { 2 } / \triangle log r / r _ { 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 by mergers . We show observational evidence that a hybrid scenario could arise also among massive galaxies . Finally , we estimated \triangle [ Z / H ] from Mg _ { 2 } and H \beta measurements and single stellar population models . The conclusions remain the same , indicating that the results can not be ascribed to age effects on Mg _ { 2 } .