  We study the fine geometric structure of bifurcation currents in the
parameter space of cubic polynomials viewed as dynamical systems. In particular
we prove that these currents have some laminar structure in a large region of
parameter space, reflecting the possibility of quasiconformal deformations. On
the other hand, there is a natural bifurcation measure, supported on the
closure of rigid parameters. We prove a strong non laminarity statement
relative to this measure.
