Abstract. In this paper we conceptually develop the theory of attogram dust grain formation by the cosmic-ray ion-enhanced brittle microerosion of atmosphereless solar system bodies. According to our theory, the multicharged cosmic ray ions penetrating into the solid material of planetary satellites, asteroids, comets and smaller space bodies give rise to microscopic cylindrical overheated zones and generate mechanical impulses and thermoelastic stresses exceeding the material tensile strength. The impulses may cause micro-scale shattering of the surfaces and the ejection of ultrafine (attogram) dust particles off the parent body. The attogram grains formed by this mechanism (the so-called track-breaking mechanism) have an average mass of 10 −19 -10 −17 g, a very flaky shape and ejection velocities of from tens to hundreds m s −1 . Depending on the ejection velocity and a large array of non-gravitational forces, such grains can deposit and accumulate on the parent body surface, orbit around the body thus forming a bound dust cocoon, or finally, escape the body as ultrafine-dust wind. Quantitative data on dust contributions to these varieties of attogram population depending on the sizes and parameters of parent body material are obtained and discussed. The volumetric track-breaking resulting in attogram grain deposition in the ice-rock mixture of cometary nuclei during the whole period of their formation is analysed. Taking the example of Halley's comet we demonstrate that the mechanism under study makes it possible to quantitatively explain the in situ measured considerable excess of attogram grains within the cometary environment in its circum-solar path sections. The problem of track-breaking disintegration of small-sized bodies in the Kuiper Belt, which are permanently subjected to a cosmic-ray ion-enhanced brittle microerosion heavier than in the Main Belt, is investigated. The track-breaking survival timescale for submicron and over hundred micron-sized grains is found to be considerably smaller than the escape timescale of the Poynting-Robertson and plasma drags, as well as the collisional mechanism. Track-breaking can also be competitive to the collisional escape in the range of grain sizes of 1 to 100 microns. A quantitative analysis of the calculations shows that the present theory may adequately explain both the observable micron/submicron dust grain depletion of the Kuiper Belt and the loss of its bulk mass during evolution. Some possible observational tests for the future revealing the predicted populations of attogram dust in the solar system are also discussed.