In this paper we study zero-noise limits of $alpha -$stable noise perturbed ODEs which are driven by an irregular vector field $A$ with asymptotics $% A(x)sim overline{a}(frac{x}{leftvert xrightvert })leftvert xrightvert ^{beta -1}x$ at zero, where $overline{a}>0$ is a continuous function and $beta in (0,1)$. The results established in this article can be considered a generalization of those in the seminal works of Bafico cite% {Ba} and Bafico, Baldi cite{BB} to the multi-dimensional case. Our approach for proving these results is inspired by techniques in cite% {PP_self_similar} and based on the analysis of an SDE for $tlongrightarrow infty $, which is obtained through a transformation of the perturbed ODE.
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