The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.