We present two-dimensional (2D) two-particle angular correlations measured with the STAR detector on relative pseudorapidity η and azimuth φ for charged particles from Au-Au collisions at √ s NN = 62 and 200 GeV with transverse momentum p t 0.15 GeV/c, |η| 1, and 2π in azimuth. Observed correlations include a same-side (relative azimuth <π/2) 2D peak, a closely related away-side azimuth dipole, and an azimuth quadrupole conventionally associated with elliptic flow. The same-side 2D peak and away-side dipole are explained by semihard parton scattering and fragmentation (minijets) in proton-proton and peripheral nucleus-nucleus collisions. Those structures follow N -N binary-collision scaling in Au-Au collisions until midcentrality, where a transition to a qualitatively different centrality trend occurs within one 10% centrality bin. Above the transition point the number of same-side and away-side correlated pairs increases rapidly relative to binary-collision scaling, the η width of the same-side 2D peak also increases rapidly (η elongation), and the φ width actually decreases significantly. Those centrality trends are in marked contrast with conventional expectations for jet quenching in a dense medium. The observed centrality trends are compared to perturbative QCD predictions computed in HIJING, which serve as a theoretical baseline, and to the expected trends for semihard parton scattering and fragmentation in a thermalized opaque medium predicted by theoretical calculations and 064902-2 ANOMALOUS CENTRALITY EVOLUTION OF TWO-. . .PHYSICAL REVIEW C 86, 064902 (2012) phenomenological models. We are unable to reconcile a semihard parton scattering and fragmentation origin for the observed correlation structure and centrality trends with heavy-ion collision scenarios that invoke rapid parton thermalization. If the collision system turns out to be effectively opaque to few-GeV partons the present observations would be inconsistent with the minijet picture discussed here.