  The purpose of this paper is to study some properties of solutions to one
dimensional as well as multidimensional stochastic differential equations (SDEs
in short) with super-linear growth conditions on the coefficients. Taking
inspiration from \cite{BEHP, KBahlali, Bahlali}, we introduce a new {\it{local
condition}} which ensures the pathwise uniqueness, as well as the non-contact
property. We moreover show that the solution produces a stochastic flow of
continuous maps and satisfies a large deviations principle of Freidlin-Wentzell
type. Our conditions on the coefficients go beyond the existing ones in the
literature. For instance, the coefficients are not assumed uniformly continuous
and therefore can not satisfy the classical Osgood condition. The drift
coefficient could not be locally monotone and the diffusion is neither locally
Lipschitz nor uniformly elliptic. Our conditions on the coefficients are, in
some sense, near the best possible. Our results are sharp and mainly based on
Gronwall lemma and the localization of the time parameter in concatenated
intervals
