Plain English Meaning
A chunk of high-altitude airspace that controllers temporarily set aside for one user — usually the military — so other aircraft are kept clear of it while the activity is underway.
Full Definition
An ATC Assigned Airspace (ATCAA) is a block of airspace, typically above FL180, that Air Traffic Control assigns to a specific user (often the military) for activities requiring separation from other IFR traffic. While active, ATC will not route other aircraft through it. It is established and released by ATC as needed, rather than being charted as permanent special use airspace.
Context Anchor
Seen when reading about civilian aircraft operating near special use airspace, especially where military activity and ATC routing may overlap.