  The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed
inter-layer dimers is studied using quantum Monte Carlo simulations. A
zero-temperature multi-critical point (p*,g*) at the classical percolation
density p=p* and inter-layer coupling g* approximately 0.16 is demonstrated.
The quantum critical exponents of the percolating cluster are determined using
finite-size scaling. It is argued that the associated finite-temperature
quantum critical regime extends to zero inter-layer coupling and could be
relevant for antiferromagnetic cuprates doped with non-magnetic impurities.
