  We discuss a limit of 3d $T_\rho^\sigma[SU(N)]$ quiver gauge theories in
which the number of nodes is large and the ranks scale quadratically with the
length of the quiver. The sphere free energies and topologically twisted
indices are obtained using supersymmetric localization. Both scale quartically
with the length of the quiver and quadratically with $N$, with trilogarithm
functions depending on the quiver data as coefficients. The IR SCFTs have
well-behaved supergravity duals in Type IIB, and the free energies match
precisely with holographic results. Previously discussed theories with $N^2\ln
N$ scaling arise as limiting cases. Each balanced 3d quiver theory is linked to
a 5d parent, whose matrix model is related and dominated by the same saddle
point, leading to close relations between BPS observables.
