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We analyze a system of cross-diffusion equations that models the growth of anavascular-tumor spheroid. The model incorporates two nonlinear diffusioneffects, degeneracy type and super diffusion. We prove the global existence ofweak solutions and justify the convergence towards the free boundary problem ofthe Hele-Shaw type when the pressure gets stiff. We also investigate theconvergence rate of the solutions in $L^1-$Lebesgue spaces.

Existence result and free boundary limit of a tumor growth model with necrotic core