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We consider two solutions of Einstein-$\Lambda$ theory which admit theextremal vanishing horizon (EVH) limit, odd-dimensional multi-spinning Kerrblack hole (in the presence of cosmological constant) and cosmological soliton.We show that the near horizon EVH geometry of Kerr has a 3d maximally symmetricsubspace whose curvature depends on rotational parameters and the cosmologicalconstant. In the Kerr-dS case, this subspace interpolates between AdS$_3$, 3dflat and dS$_3$ by varying rotational parameters, while, the near horizon ofthe EVH cosmological soliton always has a dS$_3$. The feature of the EVHcosmological soliton is that it is regular everywhere on the horizon. In thenear EVH case, these 3d parts turn into the corresponding locally maximallysymmetric spacetimes with a horizon: Kerr-dS$_3$, flat space cosmology or BTZblack hole. We show that their thermodynamics match with the thermodynamics ofthe original near EVH black holes. We also briefly discuss the holographic 2dCFT dual to the near horizon of EVH solutions.

AdS$_3$ to dS$_3$ transition in the near horizon of asymptotically de Sitter solutions