  We study the gravitational collapse of a kink within spherical symmetry and
the characteristic formulation of General Relativity. We explore some expected
but elusive gravitational collapse issues which have not been studied before in
detail, finding new features. The numerical one-parametric solution and the
structure of the spacetime are calculated using finite differences, Galerkin
collocation techniques, and some scripting for automated grid coverage. We
study the threshold of black hole formation and confirm a mass gap in the phase
transition. In the supercritical case we find a mass scaling power law
$M_{BH}={M^*_{BH}}+K[\lambda-\lambda^*]^{2\gamma}+f(K[\lambda-\lambda^*]^{2\gamma})$,
with $\gamma\approx 0.37$ independent of the initial data for the cases
considered, and $M^*_{BH}$, $K$ and $\lambda^*$ each depending on the initial
datum. The spacetime has a self-similar structure with a period of
$\Delta\approx 3.4$. In the subcritical case the Bondi mass at null infinity
decays in cascade with $\Delta/2$ interval as expected.
