  Small black holes are a powerful tool to explore infinite distances in moduli
spaces. However, we show that in 4d theories with a scalar potential growing
fast enough at infinity, it is energetically too costly for scalars to diverge
at the core, and the small black hole puffs up into a regular black hole, or
follows a runaway behaviour.
  We derive a critical exponent characterizing the occurrence or not of such
small black hole explosions, both from a 4d perspective, and in the 2d theory
after an $\bf{S}^2$ truncation. The latter setup allows a unified discussion of
fluxes, domain walls and black holes, solving an apparent puzzle in the
expression of their potentials in the 4d $\cal{N}=2$ gauged supergravity
context.
  We discuss the realization of these ideas in 4d $\cal{N}=2$ gauged
supergravities. Along the way we show that many regular black hole supergravity
solutions in the literature in the latter context are incomplete, due to
Freed-Witten anomalies (or duals thereof), and require the emission of strings
by the black hole.
  From the 2d perspective, small black hole solutions correspond to dynamical
cobordisms, with the core describing an end of the world brane. Small black
hole explosions represent obstructions to completing the dynamical cobordism.
We study the implications for the Cobordism Distance Conjecture, which states
that in any theory there should exist dynamical cobordisms accessing all
possible infinite distance limits in scalar field space. The realization of
this principle using small black holes leads to non-trivial constraints on the
4d scalar potential of any consistent theory; in the 4d $\cal{N}=2$ context,
they allow to recover from a purely bottom-up perspective, several non-trivial
properties of vector moduli spaces near infinity familiar from CY$_3$
compactifications.
