This paper is concerned with the critical quasilinear Schrödinger systems in $ {\Bbb R}^N: $
$ \left\{\begin{array}{ll}-\Delta w+(\lambda a(x)+1)w-(\Delta|w|^2)w = \frac{p}{p+q}|w|^{p-2}w|z|^q+\frac{\alpha}{\alpha+\beta}|w|^{\alpha-2}w|z|^\beta\\\ -\Delta z+(\lambda b(x)+1)z-(\Delta|z|^2)z = \frac{q}{p+q}|w|^p|z|^{q-2}z+\frac{\beta}{\alpha+\beta}|w|^\alpha|z|^{\beta-2}z, \ \end{array}\right. $
where $ \lambda>0 $ is a parameter, $ p>2, q>2, \alpha>2, \beta>2, $ $ 2\cdot(2^*-1) < p+q<2\cdot2^* $ and $ \alpha+ \beta = 2\cdot2^*. $ By using variational method, we prove the existence of positive ground state solutions which localize near the set $ \Omega = int \left\{a^{-1}(0)\right\}\cap int \left\{b^{-1}(0)\right\} $ for $ \lambda $ large enough.
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