  The interplay between site dilution and quantum fluctuations in S=1
Heisenberg antiferromagnets on the square lattice is investigated using quantum
Monte Carlo simulations. Quantum fluctuations are tuned by a single-ion
anisotropy D. In the clean limit, a sufficiently large D>D_c = 5.65(2) J forces
each spin into its m_S=0 state, and thus destabilizes antiferromagnetic order.
In the presence of site dilution, quantum fluctuations are found to destroy
N\'eel order before the percolation threshold of the lattice is reached, if D
exceeds a critical value D^* = 2.3(2) J. This mechanism opens up an extended
quantum-disordered Mott glass phase on the percolated lattice, characterized by
a gapless spectrum and vanishing uniform susceptibility.
