  We investigate the level density for several ensembles of positive random
matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a
nonhermitian random matrix. In particular, making use of the Cauchy transform,
we study free multiplicative powers of the Marchenko-Pastur (MP) distribution,
${\rm MP}^{\boxtimes s}$, which for an integer $s$ yield Fuss-Catalan
distributions corresponding to a product of $s$ independent square random
matrices, $X=X_1\cdots X_s$. New formulae for the level densities are derived
for $s=3$ and $s=1/3$. Moreover, the level density corresponding to the
generalized Bures distribution, given by the free convolution of arcsine and MP
distributions is obtained. We also explain the reason of such a curious
convolution. The technique proposed here allows for the derivation of the level
densities for several other cases.
