  We consider classes of partially hyperbolic diffeomorphism $f:M\to M$ with
splitting $TM=E^s\oplus E^c\oplus E^u$ and $\dim E^c=2$. These classes include
for instance (perturbations of) the product of Anosov and conservative surface
diffeomorphisms, skew products of surface diffeomorphisms over Anosov,
partially hyperbolic symplectomorphisms on manifolds of dimension four with
bidimensional center foliation whose center leaves are all compact. We prove
that accessibility holds in these classes for $C^1$ open and $C^r$ dense
subsets and moreover they are stably ergodic.
