We study no-hair properties of static black holes in four and higher
dimensional spacetimes with a cosmological constant. For the vanishing
cosmological constant case, we show a no-hair theorem and also a no-short-hair
theorem under certain conditions for the energy-momentum of matter fields. For
the positive cosmological constant case, we discuss conditions for hairy static
black holes to exist in terms of the energy density of matter fields evaluated
at the black hole horizon and the cosmological horizon. For the negative
cosmological constant case, we study conditions for hairy black holes by
presenting a no-hair theorem in which the asymptotic structure is assumed to be
determined by the true cosmological constant