  We analyze the branching of center vortices in $SU(3)$ Yang-Mills theory in
maximal center gauge. When properly normalized, we can define a branching
probability that turns out to be independent of the lattice spacing (in the
limited scaling window studied here). The branching probability shows a rapid
change at the deconfinement phase transition which is much more pronounced in
space slices of the lattice as compared to time slices. Though not a strict
order parameter (in the sense that it vanishes in one phase) the branching
probability is thus found to be a reliable indicator for both the location of
the critical temperature and the geometric re-arrangement of vortex matter
across the deconfinement phase transition.
