  Recent determinations of the radial distributions of mono-metallicity
populations (MMPs, i.e., stars in narrow bins in [Fe/H] within wider
[$\alpha$/Fe] ranges) by the SDSS-III/APOGEE DR12 survey cast doubts on the
classical thin - thick disk dichotomy. The analysis of these observations lead
to the non-$[\alpha$/Fe] enhanced populations splitting into MMPs with
different surface densities according to their [Fe/H]. By contrast,
$[\alpha$/Fe] enhanced (i.e., old) populations show an homogeneous behaviour.
We analyze these results in the wider context of disk formation within
non-isolated halos embedded in the Cosmic Web, resulting in a two-phase mass
assembly. By performing hydrodynamical simulations in the context of the $\rm
\Lambda CDM$ model, we have found that the two phases of halo mass assembly (an
early, fast phase, followed by a slow one, with low mass assembly rates) are
very relevant to determine the radial structure of MMP distributions, while
radial mixing has only a secondary role, depending on the coeval dynamical
and/or destabilizing events. Indeed, while the frequent dynamical violent
events occuring at high redshift remove metallicity gradients, and imply
efficient stellar mixing, the relatively quiescent dynamics after the
transition keeps [Fe/H] gaseous gradients and prevents newly formed stars to
suffer from strong radial mixing. By linking the two-component disk concept
with the two-phase halo mass assembly scenario, our results set halo
virialization (the event marking the transition from the fast to the slow
phases) as the separating event marking periods characterized by different
physical conditions under which thick and thin disk stars were born.
