  We study the statistics of the largest eigenvalues of $p \times p$ sample
covariance matrices $\Sigma_{p,n} = M_{p,n}M_{p,n}^{*}$ when the entries of the
$p \times n$ matrix $M_{p,n}$ are sparse and have a distribution with tail
$t^{-\alpha}$, $\alpha>0$. On average the number of nonzero entries of
$M_{p,n}$ is of order $n^{\mu+1}$, $0 \leq \mu \leq 1$. We prove that in the
large $n$ limit, the largest eigenvalues are Poissonian if
$\alpha<2(1+\mu^{{-1}})$ and converge to a constant in the case
$\alpha>2(1+\mu^{{-1}})$. We also extend the results of Benaych-Georges and
Peche [7] in the Hermitian case, removing restrictions on the number of nonzero
entries of the matrix.
