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We present a numerical classification of the spherically symmetric, static solutions to the Einstein-Yang-Mills equations with cosmological constant Λ. We find three qualitatively different classes of configurations, where the solutions in each class are characterized by the value of Λ and the number of nodes, n, of the Yang-Mills amplitude.For sufficiently small, positive values of the cosmological constant, Λ < Λ crit (n), the solutions generalize the Bartnik-McKinnon solitons, which are now surrounded by a cosmological horizon and approach the deSitter geometry in the asymptotic region. For a discrete set of values Λ reg (n) > Λ crit (n), the solutions are topologically 3-spheres, the ground state (n = 1) being the Einstein Universe. In the intermediate region, that is for Λ crit (n) < Λ < Λ reg (n), there exists a discrete family of global solutions with horizon and "finite size".

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