This paper introduces a spatially heterogeneous diffusive predator-prey model unifying the classical Lotka{Volterra and Holling{Tanner ones through a prey saturation coefficient, m(x), which is spatially heterogenous and it is allowed to ?degenerate'. Thus, in some patches of the territory the species can interact according to a Lotka{Volterra kinetics, while in others the prey saturation effects play a significant role on the dynamics of the species. As we are working under general mixed boundary conditions of non-classical type, we must invoke to some very recent technical devices to get some of the main results of this paper.