  The Horizon Quantum Mechanics is an approach that allows one to analyse the
gravitational radius of spherically symmetric systems and compute the
probability that a given quantum state is a black hole. We first review the
(global) formalism and show how it reproduces a gravitationally inspired GUP
relation. This results leads to unacceptably large fluctuations in the horizon
size of astrophysical black holes if one insists in describing them as
(smeared) central singularities. On the other hand, if they are extended
systems, like in the corpuscular models, no such issue arises and one can in
fact extend the formalism to include asymptotic mass and angular momentum with
the harmonic model of rotating corpuscular black holes. The Horizon Quantum
Mechanics then shows that, in simple configurations, the appearance of the
inner horizon is suppressed and extremal (macroscopic) geometries seem
disfavoured.
