In this paper we continue our analysis of arXiv:1308.1478 and study in detail the parameter space of three families of doubly spinning black ring solutions: balanced black ring, unbalanced ring and dipole-charged balanced black rings. In all these three families the Extremal Vanishing Horizon (EVH) ring appears in the vanishing limit of the dimensionful parameter of the solution which measures the ring size. We study the near horizon limit of the EVH black rings and for all three cases we find a (pinching orbifold) AdS3 throat with the AdS3 radius ℓ2 = 8G5M/(3π) where M is the ring mass and G5 is the 5d Newton constant. We also discuss the near horizon limit of near-EVH black rings and show that the AdS3 factor is replaced with a generic BTZ black hole. We use these results to extend the EVH/CFT correspondence for black rings, a 2d CFT dual to near-EVH black rings.

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