  In order to study the gravitational collapse of charged matter we analyze the
simple model of an self-gravitating massless scalar field coupled to the
electromagnetic field in spherical symmetry. The evolution equations for the
Maxwell-Klein-Gordon sector are derived in the 3+1 formalism, and coupled to
gravity by means of the stress-energy tensor of these fields. To solve
consistently the full system we employ a generalized
Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of General Relativity
that is adapted to spherical symmetry. We consider two sets of initial data
that represent a time symmetric spherical thick shell of charged scalar field,
and differ by the fact that one set has zero global electrical charge while the
other has non-zero global charge. For compact enough initial shells we find
that the configuration doesn't disperse and approaches a final state
corresponding to a sub-extremal Reissner-N\"ordstrom black hole with $|Q|<M$.
By increasing the fundamental charge of the scalar field $q$ we find that the
final black hole tends to become more and more neutral. Our results support the
cosmic censorship conjecture for the case of charged matter.
