  We present a numerical classification of the spherically symmetric, static
solutions to the Einstein--Yang--Mills equations with cosmological constant
$\Lambda$. We find three qualitatively different classes of configurations,
where the solutions in each class are characterized by the value of $\Lambda$
and the number of nodes, $n$, of the Yang--Mills amplitude. For sufficiently
small, positive values of the cosmological constant, $\Lambda < \Llow(n)$, 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 $\Lambda_{\rm reg}(n) > \Lambda_{\rm
crit}(n)$, the solutions are topologically $3$--spheres, the ground state
$(n=1)$ being the Einstein Universe. In the intermediate region, that is for
$\Llow(n) < \Lambda < \Lhig(n)$, there exists a discrete family of global
solutions with horizon and ``finite size''.
