Two-particle azimuthal ( φ) and pseudorapidity ( η) correlations using a trigger particle with large transverse momentum (p T ) in d+Au, Cu+Cu, and Au+Au collisions at √ s NN = 62.4 GeV and 200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider are presented. The near-side correlation is separated into a jet-like component, narrow in both φ and η, and the ridge, narrow in φ but broad in η. Both components are studied as a function of collision centrality, and the jet-like correlation is studied as a function of the trigger and associated p T . The behavior of the jet-like component is remarkably consistent for different collision systems, suggesting it is produced by fragmentation. The width of the jet-like correlation is found to increase with the system size. The ridge, previously observed in Au+Au collisions at √ s NN = 200 GeV, is also found in Cu+Cu collisions and in collisions at √ s NN = 62.4 GeV, but is found to be substantially smaller at √ s NN = 62.4 GeV than at √ s NN = 200 GeV for the same average number of participants ( N part ). Measurements of the ridge are compared to models.