  We study the baryonic, chemical and dynamical properties of a significantly
large sample of early proto-galaxies in the first 500 Myr of the Universe
(redshift z>9), obtained from high-resolution numerical, N-body,
hydrodynamical, chemistry simulations including atomic and molecular networks,
gas cooling, star formation, stellar evolution and metal spreading for
population III and population II-I regimes according to proper stellar yields
and lifetimes. We find that first star formation events take place in halos
with dark-matter mass M_{DM} > 2\times 10^6 M_{sun}. Early star forming objects
have: molecular fractions from x_{mol} < 10^{-4} in quiescent structures up to
x_{mol} > 0.1 in active regions; star formation rates SFR
~10^{-8}-10^{-3}M_{sun}/yr; and metallicities in the range
~10^{-8}-10^{-2}Z_{sun}. Roughly ~10% of high-z haloes host population II-I
star formation and dominate the cosmic SFR density. They usually are bursty
objects with mean specific SFR around ~10 Gyr^{-1} at z~9 and increasing with
redshift up to ~10^2 Gyr^{-1}. Stellar feedback effects alter the baryonic
content of the haloes and locally affect their chemical and thermo-dynamical
properties, as reflected by the broadening of various physical relations. The
establishment of gaseous rotationally-supported cores is quite uncommon, weakly
related to the large-scale dark-matter behaviour and evolving in an
intermittent fashion. The colder, molecular-rich phase tends to maintain any
established rotational motion longer with respect to the hotter, metal-rich
component, which is very sensitive to environmental processes. While the
fraction of haloes featuring a significant amount of co-rotating,
molecular-rich gas increases with cosmic time (from a few percent at z~20 up to
~5-15% at z~9), the chaotic nature of metal-enriched material does not lead to
particular trends.
