  Here we investigate the evolution of a Milky Way (MW) -like galaxy with the
aim of predicting the properties of its progenitors all the way from $z \sim
20$ to $z = 0$. We apply GAMESH (Graziani et al. 2015) to a high resolution
N-Body simulation following the formation of a MW-type halo and we investigate
its properties at $z \sim 0$ and its progenitors in $0 < z < 4$. Our model
predicts the observed galaxy main sequence, the mass-metallicity and the
fundamental plane of metallicity relations in $0 < z < 4$. It also reproduces
the stellar mass evolution of candidate MW progenitors in $0 \lesssim z
\lesssim 2.5$, although the star formation rate and gas fraction of the
simulated galaxies follow a shallower redshift dependence. We find that while
the MW star formation and chemical enrichment are dominated by the contribution
of galaxies hosted in Lyman $\alpha$-cooling halos, at z > 6 the contribution
of star forming mini-halos is comparable to the star formation rate along the
MW merger tree. These systems might then provide an important contribution in
the early phases of reionization. A large number of mini-halos with old stellar
populations, possibly Population~III stars, are dragged into the MW or survive
in the Local Group. At low redshift dynamical effects, such as halo mergers,
tidal stripping and halo disruption redistribute the baryonic properties among
halo families. These results are critically discussed in light of future
improvements including a more sophisticated treatment of radiative feedback and
inhomogeneous metal enrichment.
