A quantum system behaves classically when quantum probabilities are high for coarse-grained histories correlated in time by deterministic laws. That is as true for the flight of a tennis ball as for the behavior of spacetime geometry in gravitational collapse. Classical spacetime may be available only in patches of configuration space with quantum transitions between them. Global structures of general relativity. such as event horizons may not be available.
We consider the quantum dynamics of gravitational collapse in a model in which classical spacetime breaks down because the wave function spreads over a large ensemble of classical end states as envisioned in the fuzzball proposal. Probabilities of coarse-grained observables are highly peaked around the classical black hole values. By contrast, probabilities for finer-grained observables probing the near horizon region are broadly distributed, and no notion of `averaging' applies. This means that the formation of fuzzballs may result significant observational features including a novel type of gravitational wave burst associated with tunneling between classical solutions.