  As the only gravity theory with quadratic curvature terms and second-order
field equations, Einstein-dilaton-Gauss-Bonnet gravity is a natural testbed to
probe the high-curvature regime beyond General Relativity in a fully
nonperturbative way. Due to nonperturbative effects of the dilatonic coupling,
black holes in this theory have a minimum mass which separates a stable branch
from an unstable one. The minimum mass solution is a double point in the phase
diagram of the theory, wherein the critical black hole and a wormhole solution
coexist. We perform extensive nonlinear simulations of the spherical collapse
onto black holes with scalar hair in this theory, especially focusing on the
region near the minimum mass. We study the nonlinear transition from the
unstable to the stable branch and assess the nonlinear stability of the latter.
Furthermore, motivated by modeling the mass loss induced by Hawking radiation
near the minimum mass at the classical level, we study the collapse of a
phantom field onto the black hole. When the black-hole mass decreases past the
critical value, the apparent horizon shrinks significantly, eventually
unveiling a high-curvature elliptic region. We argue that evaporation in this
theory is bound to either violate the weak cosmic censorship or produce
horizonless remnants. Addressing the end-state might require a different
evolution scheme.
