  We extend Penrose's peeling model for the asymptotic behaviour of solutions
to the scalar wave equation at null infinity on asymptotically flat
backgrounds, which is well understood for flat space-time, to Schwarzschild and
the asymptotically simple space-times of Corvino-Schoen/Chrusciel-Delay. We
combine conformal techniques and vector field methods: a naive adaptation of
the ``Morawetz vector field'' to a conformal rescaling of the Schwarzschild
metric yields a complete scattering theory on Corvino-Schoen/Chrusciel-Delay
space-times. A good classification of solutions that peel arises from the use
of a null vector field that is transverse to null infinity to raise the
regularity in the estimates. We obtain a new characterization of solutions
admitting a peeling at a given order that is valid for both Schwarzschild and
Minkowski space-times. On flat space-time, this allows large classes of
solutions than the characterizations used since Penrose's work. Our results
establish the validity of the peeling model at all orders for the scalar wave
equation on the Schwarzschild metric and on the corresponding
Corvino-Schoen/Chrusciel-Delay space-times.
