  We prove that given any $\theta_1,\ldots,\theta_{2d-2}\in \R\setminus\Z$, the
support of the bifurcation measure of the moduli space of degree $d$ rational
maps coincides with the closure of classes of maps having $2d-2$ neutral cycles
of respective multipliers $e^{2i\pi\theta_1},\ldots,e^{2i\pi\theta_{2d-2}}$. To
this end, we generalize a famous result of McMullen, proving that homeomorphic
copies of $(\partial \Mand)^{k}$ are dense in the support of the
$k^{th}$-bifurcation current $T^k_\bif$ in general families of rational maps,
where $\Mand$ is the Mandelbrot set. As a consequence, we also get sharp
dimension estimates for the supports of the bifurcation currents in any family.
