  We have studied the static and dynamic magnetic properties of two-dimensional
(2D) and quasi-two-dimensional, spin-S, quantum Heisenberg antiferromagnets
(QHAF) diluted with spinless vacancies. Using spin-wave theory and T-matrix
approximation we have calculated the staggered magnetization, M(x,T), the
neutron scattering dynamical structure factor, S(k,omega), the 2D magnetic
correlation length, \xi(x,T), and the Neel temperature, T_N(x), for the
quasi-2D case. We find that in 2D the hydrodynamic description of excitations
in terms of spin-waves breaks down at the wavelength larger than \ell/a ~
exp(\pi/4x), x being impurity concentration and "a" the lattice spacing. The
density of states acquires a constant term and exhibits an anomalous peak at
omega omega_0 associated with the low-energy localized excitations. These
anomalies lead to a substantial enhancement of the magnetic specific heat, C_M,
at low temperatures. Although the dynamical properties are significantly
modified we show that 2D is not the lower critical dimension for this problem.
Our results are in quantitative agreement with the recent Monte Carlo
simulations and experimental data for S=1/2, S=1, and S=5/2.
