  We discuss the effect of site dilution on both the magnetization and the
density of states of quantum spins in the honeycomb lattice, described by the
antiferromagnetic Heisenberg spin-S model. For this purpose a real-space
Bogoliubov-Valatin transformation is used. In this work we show that for the
S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin
S=1/2, however, the linear spin wave approximation breaks down. In this case,
we have studied the effect of dilution on the staggered magnetization using the
Stochastic Series Expansion Monte Carlo method. Two main results are to be
stressed from the Monte Carlo method: (i) a better value for the staggered
magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the
staggered magnetization of the percolating cluster at the classical percolation
threshold, showing that there is no quantum critical transition driven by
dilution in the Heisenberg model. In the solution of the problem using linear
the spin wave method we pay special attention to the presence of zero energy
modes. Using a combination of linear spin wave analysis and the recursion
method we were able to obtain the thermodynamic limit behavior of the density
of states for both the square and the honeycomb lattices. We have used both the
staggered magnetization and the density of states to analyze neutron scattering
experiments and Neel temperature measurements on quasi-two- -dimensional
honeycomb systems. Our results are in quantitative agreement with experimental
results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.
