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
  diffusion and the superdiffusion are provided.