Robinson-Trautman space-times of Petrov type II with a cosmological constant #LAMBDA# and mass parameter m > 0 are studied. They are shown to approach the corresponding spherically symmetric Schwarzschild- (anti)-de Sitter solution at large retarded times. Their global structure is analyzed, and it is demonstrated that the smoothness of the extension across the horizon, as compared with the case #LAMBDA#=0, can increase for #LAMBDA# > 0 and decreases for #LAMBDA# < 0. fOR THE EXTREME VALUE 9#LAMBDA#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 and may serve as test beds in numerical studies of more realistic situations.
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