  We analyze the structure of heavy multitrace BPS operators in N = 1
superconformal quiver gauge theories that arise on the worldvolume of D3-branes
on an affine toric cone. We exhibit a geometric procedure for counting heavy
mesonic operators with given U(1) charges. We show that for any fixed linear
combination of the U(1) charges, the entropy is maximized when the charges are
in certain ratios. This selects preferred directions in the charge space that
can be determined with the help of a piece of string. We show that almost all
heavy mesonic operators of fixed U(1) charges share a universal structure. This
universality reflects the properties of the dual extremal black holes whose
microstates they create. We also interpret our results in terms of typical
configurations of dual giant gravitons in AdS space.
