  We initiate the mathematical study of spherical collapse of self-gravitating
charged scalar fields. The main result gives a complete characterization of the
future boundary of spacetime, providing a starting point for studying the
cosmic censorship conjectures. In general, the boundary includes two null
components, one emanating from the center of symmetry and the other from the
future limit point of null infinity, joined by an achronal component to which
the area-radius function r extends continuously to zero. Various components of
the boundary, a priori, may be empty and establishing such generic emptiness
would suffice to prove formulations of weak or strong cosmic censorship. As a
simple corollary of the boundary characterization, the present paper rules out
scenarios of 'naked singularity' formation by means of 'super-charging'
(near-)extremal Reissner-Nordstr\"om black holes. The main difficulty in
delimiting the boundary is isolated in proving a suitable global extension
principle that effectively excludes a broad class of singularity formation.
This suggests a new notion of 'strongly tame' matter models, which we introduce
in this paper. The boundary characterization proven here extends to any such
'strongly tame' Einstein-matter system.
