  We present a genealogy for superprocesses with a non-homogeneous quadratic
branching mechanism, relying on a weighted version of the superprocess and a
Girsanov theorem. We then decompose this genealogy with respect to the last
individual alive (William's decomposition). Letting the extinction time tend to
infinity, we get the Q-process by looking at the superprocess from the root,
and define another process by looking from the top. Examples including the
multitype Feller diff usion and the superdiffusion are provided.
