  We investigate the continuum q-Potts model at its transition point from the
disordered to the ordered regime, with particular emphasis on the coexistence
of disordered and ordered phases in the high-q case. We argue that occurrence
of phase transition can be seen as percolation in the related random cluster
representation, similarly to the lattice Potts model, and investigate the
typical structure of clusters for high q. We also report on numerical
simulations in two dimensions using a continuum version of the Swendsen-Wang
algorithm, compare the results with earlier simulations which used the invaded
cluster algorithm, and discuss implications on the geometry of clusters in the
disordered and ordered phases.
