  Using new long-slit spectroscopy obtained with X-Shooter at ESO-VLT, we
study, for the first time, radial gradients of optical and Near-Infrared
IMF-sensitive features in a representative sample of galaxies at the very
high-mass end of the galaxy population. The sample consists of seven early-type
galaxies (ETGs) at $z\sim0.05$, with central velocity dispersion in the range
$300<\sigma<350$km/s. Using state-of-art stellar population synthesis models,
we fit a number of spectral indices, from different chemical species (including
TiO's and Na indices), to constrain the IMF slope (i.e. the fraction of
low-mass stars), as a function of galactocentric distance, over a radial range
out to $\sim4$kpc. ETGs in our sample show a significant correlation of IMF
slope and surface mass density. The bottom-heavy population (i.e. an excess of
low-mass stars in the IMF) is confined to central galaxy regions with surface
mass density above $\sim 10^{10} M_\odot kpc^{-2}$, or, alternatively, within a
characteristic radius of $\sim2$~kpc. Radial distance, in physical units, and
surface mass density, are the best correlators to IMF variations, with respect
to other dynamical (e.g. velocity dispersion) and stellar population (e.g.
metallicity) properties. Our results for the most massive galaxies suggest that
there is no single parameter} that fully explains variations in the stellar
IMF, but IMF radial profiles at z$\sim$0 rather result from the complex
formation and mass accretion history of galaxy inner and outer regions.
