  A regular solution of the system of coupled equations of the nonlinear
electrodynamics and gravity describing static and spherically-symmetric black
holes in an asymptotically de Sitter universe is constructed and analyzed.
Special emphasis is put on the degenerate configurations (when at least two
horizons coincide) and their near horizon geometry. It is explicitly
demonstrated that approximating the metric potentials in the region between the
horizons by simple functions and making use of a limiting procedure one obtains
the solutions constructed from maximally symmetric subspaces with different
absolute values of radii. Topologically they are $AdS_{2}\times S^{2}$ for the
cold black hole, $dS_{2}\times S^{2}$ when the event and cosmological horizon
coincide, and the Pleba\'nski- Hacyan solution for the ultraextremal black
hole. A physically interesting solution describing the lukewarm black holes is
briefly analyzed
