  We discuss magnetic monopole solutions of the Einstein-Yang-Mills-Higgs
equations with a positive cosmological constant. These configurations approach
asymptotically the de Sitter spacetime background and exist only for a nonzero
Higgs potential. We find that the total mass of the solutions within the
cosmological horizon is finite. However, their mass evaluated by using the
surface counterterm method outside the cosmological horizon at early/late time
infinity generically diverges. Magnetic monopole solutions with finite mass and
noninteger charge are found however in a truncation of the theory with a
vanishing Higgs field. Both solutions with a regular origin and cosmological
black holes are studied, special attention being paid to the computation of the
global charges.
