The hexagonal oxygen superlattice H(root 3 x root 3) phase of RCuO(2.6
6) delafossite-type compounds, R=La or Y, provides a unique example of
an s=1/2 diluted kagome system. We perform a theoretical study of the
magnetic properties of this lattice, both in the insulating and the m
etallic cases. We attribute to the particular topology the absence of
magnetic order experimentally observed down to low temperatures. The r
oles of longer-range interactions, defects, and quantum effects are di
scussed.