Comets, comet-like objects and their fragments are the most plausible source for the dust in both the inner heliosphere and planetary debris discs around other stars. The smallest size of dust particles in debris discs is not known and recent observational results suggest that the size distribution of the dust extends down to sizes of a few nanometres or a few tens of nanometres. In the Solar System, electric field measurements from spacecraft observe events that are explained with high-velocity impacts of nanometre-sized dust. In some planetary debris discs an observed mid- to near-infrared emission supposedly results from hot dust located in the vicinity of the star. And the observed emission is characteristic of dust of sizes a few tens of nanometres. Rosetta observations, on the other hand, provide little information on the presence of nanodust near comet 67P/Churyumov–Gerasimenko. This article describes why this is not in contradiction to the observations of nanodust in the heliosphere and in planetary debris discs. The direct ejection of nanodust from the nucleus of the comet would not contribute significantly to the observed nanodust fluxes. We discuss a scenario that nanodust forms in the interplanetary dust cloud through the high-velocity collision process in the interplanetary medium for which the production rates are highest near the Sun. Likewise, fragmentation by collisions occurs near the star in planetary debris discs. The collisional fragmentation process in the inner Solar System occurs at similar velocities to those of the collisional evolution in the interstellar medium. A question for future studies is whether there is a common magic size of the smallest collision fragments and what determines this size. This article is part of the themed issue ‘Cometary science after Rosetta’.