  We study partially hyperbolic sets of C1-diffeomorphisms. For these sets
there are defined the strong stable and strong unstable laminations. A
lamination is called dynamically minimal when the orbit of each leaf intersects
the set densely. We prove that partially hyperbolic sets having a dynamically
minimal lamination have empty interior. We also study the Lebesgue measure and
the spectral decomposition of these sets. These results can be ap- plied to
C1-generic/robustly transitive attractors with one-dimensional center bundle.
