Quantum gravitational effects in black hole spacetimes with a cosmological constant ¿ are considered. The effective quantum spacetimes for the black holes are constructed by taking into account the renormalization group improvement of classical solutions obtained in the framework of unimodular gravity (a theory which is identical to general relativity at a classical level). This allows us to avoid the usual divergences associated with the presence of a running ¿. The horizons and causal structure of the improved black holes are discussed, taking into account the current observational bounds for the cosmological constant. It is shown that the resulting effective quantum black hole spacetimes are always devoid of singularities.

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