  This paper gives a complete classification of the possible ergodic
decompositions for certain open families of volume-preserving partially
hyperbolic diffeomorphisms. These families include systems with compact center
leaves and perturbations of Anosov flows under conditions on the dimensions of
the invariant subbundles. The paper further shows that the non-open
accessibility classes form a $C^1$ lamination and gives results about the
accessibility classes of non-volume-preserving systems.
  Note: this document has been modified slightly from earlier preprints. The
numbering of sections was changed to match the published version and an erratum
has been added to the end.
