Azalea NaiSmith, an Asteroid Brain in the Tau Ceti system
The A-brain is, in short, a small body (smaller than a Moon Brain) that has been partially converted to computronium. The term is something of a colloquialism because unlike its larger brethren, the Moon Brain and Jupiter Brain, most asteroid brains do not consist entirely of computronium. The mass of a moderate-sized asteroid is insufficient to support an S3 intellect (unless very advanced computronium is used) but more than enough mass for an S1 or S2. Instead, much of the mass of the asteroid is reserved for other purposes, such as manufacturing, or data storage, or even accommodation for modosophonts.
A classic A-brain, as opposed to an AI's asteroid facility, will thoroughly integrate the entire mass into its sensorium as if it is an extension of its body. In other terms, the A-brain is a mini-ISO that an AI will gradually develop to suit its needs and whims. Many seem satisfied in joining in computational complexes around gas giants or in asteroid belts, such as Kenehan-LeRiche complexes, while others develop into mobile vessels to explore the galaxy.