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We study the spherically symmetric Einstein–Maxwell system coupled to a real scalar field. In this model, solutions either disperse or form a black hole. We give a precise description of the dynamics in the infinite-dimensional moduli space of initial data near the Reissner–Nordström family. In particular, we prove that the boundary in the moduli space between dispersion and black hole formation is a smooth hypersurface consisting of initial data whose evolutions converge to an extremal Reissner–Nordström black hole. Near this threshold, we quantify transient horizon instabilities and establish universal scaling laws for the horizon area, horizon location, and temperature. This is joint work with Yannis Angelopoulos (BIMSA) and Ryan Unger (Berkeley).