  The possibility of stable or quasi--stable Planck mass black hole remnants as
solution to the black hole information paradox is commonly believed
phenomenologically unacceptable: since we have to expect a black hole remnant
for every possible initial state, the number of remnants should be infinite.
This would lead to remnant pair production in any physical process with a total
available energy roughly exceeding the Planck mass, against trivial evidences.
In this note I point out that the number of remnants in our Universe could be
finite, at least if the value of the cosmological constant is positive, as
present observational data could indicate. Nevertheless, it is not clear if a
huge but finite number of states is phenomenologically allowed.
