Nanometre-sized diamond has been found in meteorites(1), protoplanetary nebulae(2) and interstellar dusts(3), as well as in residues of detonation(4) and in diamond films(5,6). Remarkably, the size distribution of diamond nanoparticles seems to be peaked around 2-5 nm, and to be largely independent of preparation conditions. We have carried out ab initio calculations of the stability of nanodiamond as a function of surface hydrogen coverage and of size. We have found that at about 3 nm, and for a broad range of pressures and temperatures, particles with bare, reconstructed surfaces become thermodynamically more stable than those with hydrogenated surfaces, thus preventing the formation of larger grains. Our findings provide an explanation of the size distribution of extraterrestrial and of terrestrial nanodiamond found in ultradispersed and ultracrystalline diamond films. They also provide an atomistic structural model of these films, based on the topology and structure of 2-3-nm dimond clusters consisting of a diamond core surrounded by a fullerene-like carbon network(7).