A quantum bound on the compactness

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also com- ment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the cor- puscular picture of black holes.