  It is known that volume hyperbolicity (partial hyperbolicity and uniform
expansion or contraction of the volume in the extremal bundles) is a necessary
condition for robust transitivity or robust chain recurrence hence for
tameness. In this paper, on any 3-manifold we build examples of
quasi-attractors which are volume hyperbolic and wild at the same time. As a
main corollary, we see that, for any closed 3-manifold $M$, the space
$\mathrm{Diff}^1(M)$ admits a non-empty open set where every $C^1$-generic
diffeomorphism has no attractors or repellers.
  The main tool of our construction is the notion of flexible periodic points
introduced by the authors. For ejecting the flexible points from the
quasi-attractor, we control the topology of the quasi-attractor using the
notion of partially hyperbolic filtrating Markov partition, which we introduce
in this paper.
