  We have studied the doping dependence of the in-plane and out-of-plane
superfluid density, \rho^s(0), of two monolayer high-Tc superconductors,
HgBa_2CuO_{4+\delta} and La_{2-x}Sr_xCuO_4, using the low frequency
ac-susceptibility and the muon spin relaxation techniques. For both
superconductors, \rho^s(0) increases rapidly with doping in the under- and
optimally doped regime and becomes nearly doping independent above a critical
doping, p_c = 0.20.
