  By fixing lattice Yang-Mills configurations to the maximal center gauge and
subsequently applying the technique of center projection, one can identify
center vortices in these configurations. Recently, center vortices have been
shown to determine the string tension between static quarks at finite
temperatures (center dominance); also, they correctly reproduce the deconfining
transition to a phase with vanishing string tension. After verifying center
dominance also for the so-called spatial string tension, the present analysis
focuses on the global topology of vortex networks. General arguments are given
supporting the notion that the deconfinement transition in the center vortex
picture takes the guise of a percolation transition. This transition is
detected in Monte Carlo experiments by concentrating on various slices through
the closed vortex surfaces; these slices, representing loops in lattice
universes reduced by one dimension, clearly exhibit the expected transition
from a percolating to a non-percolating, deconfined, phase. The latter phase
contains a large proportion of vortex loops winding around the lattice in the
Euclidean time direction. At the same time, an intuitive picture clarifying the
persistence of the spatial string tension in the deconfined phase emerges.
