  We stress that, although the $D^*$ is very narrow (one hundred of keV), the
difference between the full $D^*$ contribution to $B \to \bar{D} \pi \pi$ and
its zero width limit, which stems from the resonance tail, is surprisingly
large~: several percents. This phenomenon is a general effect which appears
when considering the production of particles that are coupled to an
intermediate virtual state, stable or not, and it persists whether the width is
large or not. The effects of various cuts and of the inclusion of damping
factors at the strong and weak vertices are discussed. It is shown how the zero
width limit, needed to compare with theoretical expectations, can be extracted.
One also evaluates the virtual $D^*_V$ contribution, which comes out roughly as
expected from theory, but which is however much more dependent on cuts and
uncontrollable "off-shell" effects. We suggest a way to estimate the impact of
the damping factors.
