  In this paper we are concerned with nonlinear Schr\"odinger equations with
random potentials. Our class includes continuum and discrete potentials.
Conditions on the potential $V_{\omega}$ are found for existence of solutions
almost sure $\omega $. We study probabilistic properties like central limit
theorem and law of larger numbers for the obtained solutions by independent
ensembles. We also give estimates on the expected value for the
$L^{\infty}$-norm of the solution showing how it depends on the size of the
potential.
