Second order perturbation theory and a Lipkin–Nogami scheme combined with an exact Monte Carlo projection after variation are applied to compute the ground-state energy of 6≤N≤210 electron–hole pairs confined in a parabolic two-dimensional quantum dot. The energy shows nice scaling properties as N or the confinement strength is varied. A crossover from the high-density electron–hole phase to the BCS excitonic phase is found at a density which is roughly four times the close-packing density of excitons.