  In this paper, we investigate the asymptotic spectrum of complex or real
Deformed Wigner matrices $(M_N)_N$ defined by $M_N=W_N/\sqrt{N}+A_N$ where
$W_N$ is an $N\times N$ Hermitian (resp., symmetric) Wigner matrix whose
entries have a symmetric law satisfying a Poincar\'{e} inequality. The matrix
$A_N$ is Hermitian (resp., symmetric) and deterministic with all but finitely
many eigenvalues equal to zero. We first show that, as soon as the first
largest or last smallest eigenvalues of $A_N$ are sufficiently far from zero,
the corresponding eigenvalues of $M_N$ almost surely exit the limiting
semicircle compact support as the size $N$ becomes large. The corresponding
limits are universal in the sense that they only involve the variance of the
entries of $W_N$. On the other hand, when $A_N$ is diagonal with a sole simple
nonnull eigenvalue large enough, we prove that the fluctuations of the largest
eigenvalue are not universal and vary with the particular distribution of the
entries of $W_N$.
