  Dilution effects on spin-1/2 quantum Heisenberg antiferromagnets with a
non-magnetic spin-gapped ground state are studied by means of the qunatum Monte
Carlo simulation. In the site-diluted system, an antiferromagnetic long-range
order (AF-LRO) is induced at an infinitesimal concentration of dilution due to
an effective coupling $\tilde{J}_{mn}$ between induced magnetic moments. In the
bond-diluted case, on the other hand, the AF-LRO is not induced up to a certain
concentration of dilution due to singlet pairs reformed by an AF coupling
$\tilde{J}_{\rm af}$ between the edge spins of the diluted bond through the
two-dimensional shortest paths. The competition between $\tilde{J}_{mn}$ and
$\tilde{J}_{\rm af}$ yields peculiar phenomena in the bond-diluted system.
