We present here some results from the numerical evolution of spherically symmetric and axisymmetric spacetimes. Two basic aspects were common in the cases we have treated: first, the field equations are in the characteristic formulation, and second, we have employed the spectral methods to solve the numerically the field equations. In the spherical case black holes are produced as the result of the collapse of scalar fields. The whole spectrum of black hole masses which ranges from infinitesimal to large values are obtained after varying the amplitude of the initial scalar field distribution. Then, we have found strong numerical evidence that this spectrum is described by a nonextensive distribution law. Concerning axisymmetric spacetimes we have integrated the field equations of Robinson-Trautman space times with a new and efficient code. We have applied the code to describe in a simple scenario the non-frontal collision of two black holes. Finally, a more realistic framework represented by the field equations of the Bondi problem were considered.
