  Robinson-Trautman radiative space-times of Petrov type II with a
non-vanishing cosmological constant Lambda and mass parameter m>0 are studied
using analytical methods. They are shown to approach the corresponding
spherically symmetric Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter
solution at large retarded times. Their global structure is analyzed, and it is
demonstrated that the smoothness of the extension of the metrics across the
horizon, as compared with the case Lambda=0, is increased for Lambda>0 and
decreased for Lambda<0. For the extreme value 9Lambda m^2=1, the extension is
smooth but not analytic. This case appears to be the first example of a smooth
but not analytic horizon. The models with Lambda>0 exhibit explicitly the
cosmic no-hair conjecture under the presence of gravitational waves.
