Kondo Lattice without Nozieres Exhaustion Effect

We discuss the properties of layered Anderson/Kondo lattices with metallic electrons confined in 2D xy planes and local spins in insulating layers forming chains in z direction. Each spin in this model possesses its own 2D Kondo cloud, so that the Nozieres' exhaustion problem does not occur. The excitation spectrum of the model is gapless both in charge and spin sectors. The disordered phases and possible experimental realizations of the model are briefly discussed.