  We decompose the genealogy of a general superprocess with spatially dependent
branching mechanism with respect to the last individual alive (Williams
decomposition). This is a generalization of the main result of Delmas and
H\'{e}nard [Electron. J. Probab.,18,1-43,2013] where only superprocesses with
spatially dependent quadratic branching mechanism were considered. As an
application of the Williams decomposition, we prove that, for some
superprocesses, the normalized total mass will converge to a point mass at its
extinction time. This generalizes a result of Tribe [Ann.
Probab.,20,286-311,1992] in the sense that our branching mechanism is more
general.
