  We consider the class of partially hyperbolic diffeomorphisms $f:M\to M$
obtained as the discretization of topological Anosov flows. We show uniqueness
of minimal unstable lamination for these systems provided that the underlying
Anosov flow is transitive and not orbit equivalent to a suspension. As a
consequence, uniqueness of quasi-attractors is obtained. If the underlying
Anosov flow is not transitive we get an analogous finiteness result provided
that the restriction of the flow to any of its attracting basic pieces is not a
suspension. A similar uniqueness result is also obtained for certain
one-dimensional center skew-products.
