Context. Understanding the detailed structure of the interstellar gas is essential for our knowledge of the star formation process.Aim. 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.Methods. 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 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.Results. The cores’ properties show encouraging agreements with observations. The mass spectrum presents a clear powerlaw at high masses with an exponent close to ≃−1.3 and a peak at about 1–2 M⊙. 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 ratios, typically between ≃0.3 and 3 indicating that they are significantly magnetized. Investigating the time and spatial dependence of these statistical properties, we conclude that they are not significantly affected by the zooming procedure and that they do not present very large fluctuations. The most severe issue appears to be the dependence on the numerical resolution of the core mass function (CMF). While the core definition process may possibly introduce some biases, the peak tends to shift to smaller values when the resolution improves.Conclusions. Our simulations, which use self-consistently generated initial conditions at the kpc scale, produce a large number of prestellar cores from which reliable statistics can be inferred. Preliminary comparisons with observations show encouraging agreements. In particular the inferred CMFs resemble the ones inferred from recent observations. We stress, however, a possible issue with the peak position shifting with numerical resolution.