LAUSR

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.