  All superconformal quivers are shown to satisfy the relation c = a and are
thus good candidates for being the field theory living on D3 branes probing CY
singularities. We systematically study 3 block and 4 block chiral quivers which
admit a superconformal fixed point of the RG equation. Most of these theories
are known to arise as living on D3 branes at a singular CY manifold, namely
complex cones over del Pezzo surfaces. In the process we find a procedure of
getting a new superconformal quiver from a known one. This procedure is termed
"shrinking" and, in the 3 block case, leads to the discovery of two new models.
Thus, the number of superconformal 3 block quivers is 16 rather than the
previously known 14. We prove that this list exausts all the possibilities. We
suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be
obtained by shrinking a del Pezzo quiver and verify this statement for all 4
block quivers, where a lot of "shrunk'' del Pezzo models exist.
