The frequency, semi-major axis, and mass distribution of stellar companions likely depend on the mass of the primaries and on the environment where the stars form. These properties are very different for early- and late-type stars. However, data are largely incomplete, even for the closest environments to the Sun, preventing a cleaner view of the problem. This paper provides basic information about the properties of companions to B stars in the Scorpius-Centaurus association (age ~15Myr); this is the closest association containing a large population of 181 B-stars. We gathered available data combining high contrast imaging samples from BEAST, SHINE, and previous surveys with evidence of companions from Gaia (both through direct detection and astrometry), from eclipsing binaries, and from spectroscopy. We evaluated the completeness of the binary search and estimated the mass and semi-major axis for all detected companions. These data provide a complete sample of stellar secondaries (extending well in the substellar regime) for separation >3au, and they are highly informative as to closer companions. We found evidence for 200 companions around 181 stars. We did not find evidence for companions for only 43 (23.8+/-3.6%) of the targets, with the fraction being as low as 15.2+/-4.1% for stars with M_A_>3.5M_{sun}_ while it is 31.5+/-5.9% for lower-mass stars. This confirms earlier findings for a clear trend of a binary fraction with stellar mass. The median semi-major axis of the orbits of the companions is smaller for B than in A stars, confirming a turn-over previously found for OB stars. The mass distribution of the very wide (a>1000au) and closer companions is different. Very few companions of massive stars M_A_>5.0M_{sun}_ have a mass below solar and even fewer are M stars with a semi-major axis <1000au. However, the scarcity of low-mass companions extends throughout the whole sample. Period and mass ratio distributions are different for early B stars (up to B7 spectral type) and stars of a later spectral type: most early B stars are in compact systems with massive secondaries, while less massive stars are mainly in wider systems with a larger spread in mass ratios. We derived log-normal fits to the distribution of the semi-major axis and mass ratios for low and high-mass B stars; these relations suggest that it is not probable that the planets and brown dwarf (BD) companions to b Cen and mu2 Sco are extreme cases in the distribution of stellar companions. We interpret our results as the formation of secondaries with a semi-major axis <1000au (about 80% of the total) by fragmentation of the disk of the primary and selective mass accretion on the secondaries. The formation of secondaries within the disk of primaries in close binaries has been proposed by many others before; it unifies the scenarios for formation of close binaries with that of substellar companions that also form within the primary disk, though on a different timescale. We also find that the observed trends with primary mass may be explained by a more prolonged phase of accretion episodes on the disk and by a more effective inward migration. Finally, in the Appendices we describe the detection of twelve new stellar companions from the BEAST survey and of a new BD companion at 9.599 arcsec from HIP 74752 using Gaia data, and we discuss the cases of possible BD and low-mass stellar companions to HIP 59173, HIP 62058, and HIP 64053.