  A 1D model hamiltonian that is motivated by the recent discovery of the
heavy-fermion behavior in the cuprates of the $Nd_2CuO_4$ type is studied. It
consists of $t-J$ interacting conduction electrons coupled to a lattice of
localized spins through a Kondo exchange term $J_K$. Exact diagonalization and
density matrix renormalization group methods are used. The latter method is
generalized to arbitrary densities. At half-filling, a spin gap opens for all
$J_K>0$. Away from half-filling$,$ it is shown that, at strong $J_K$% , the
ground state is an unsaturated ferromagnet . At weak $J_K$ the system is in a
paramagnetic phase with enhanced RKKY correlations. The importance of
self-screening of the local moments in the depletion regime is discussed. We
argue that these findings transcend the specifics of the model.
