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Abridged. Understanding the detailed structure of the interstellar gas isessential for our knowledge of the star formation process. The small-scalestructure of the interstellar medium (ISM) is a direct consequence of thegalactic scales and making the link between the two is essential. We performadaptive mesh simulations that aim to bridge the gap between the intermediategalactic scales and the self-gravitating prestellar cores. For this purpose weuse stratified supernova regulated ISM magneto-hydrodynamical (MHD) simulationsat the kpc scale to set up the initial conditions. We then zoom, performing aseries of concentric uniform refinement and then refining on the Jeans lengthfor 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 variouscriteria based on virial analysis. Their most relevant properties are computedand, due to the large number of objects formed in the simulations, reliablestatistics are obtained. The cores properties show encouraging agreements withobservations. The mass spectrum presents a clear powerlaw at high masses withan exponent close to $\simeq -1.3$ and a peak at about 1-2 $M_\odot$. Thevelocity dispersion and the angular momentum distributions are respectively afew times the local sound speed and a few $10^{-2}$ pc km s$^{-1}$. We alsofind that the distribution of thermally supercritical cores present a range ofmagnetic mass-to-flux over critical mass-to-flux ratio which typically rangesbetween $\simeq$0.3 and 3.

The FRIGG project: From intermediate galactic scales to self-gravitating cores