  Abridged. Understanding the detailed structure of the interstellar gas is
essential for our knowledge of the star formation process. The small-scale
structure of the interstellar medium (ISM) is a direct consequence of the
galactic scales and making the link between the two is essential. We perform
adaptive mesh simulations that aim to bridge the gap between the intermediate
galactic scales and the self-gravitating prestellar cores. For this purpose we
use stratified supernova regulated ISM magneto-hydrodynamical (MHD) simulations
at the kpc scale to set up the initial conditions. We then zoom, performing a
series of concentric uniform refinement and then refining on the Jeans length
for the last levels. This allows us to reach a spatial resolution of a few
$10^{-3}$ pc. The cores are identified using a clump finder and various
criteria based on virial analysis. Their most relevant properties are computed
and, due to the large number of objects formed in the simulations, reliable
statistics are obtained. The cores properties show encouraging agreements with
observations. The mass spectrum presents a clear powerlaw at high masses with
an exponent close to $\simeq -1.3$ and a peak at about 1-2 $M_\odot$. The
velocity dispersion and the angular momentum distributions are respectively a
few times the local sound speed and a few $10^{-2}$ pc km s$^{-1}$. We also
find that the distribution of thermally supercritical cores present a range of
magnetic mass-to-flux over critical mass-to-flux ratio which typically ranges
between $\simeq$0.3 and 3.
