  Thanks to the 9 contacts deposited on the surface of a high quality YBCO
twinned single crystal, we investigate both vortex guided motion along twins
and the mixed state Hall effect. Firstly, we clearly identify the vortex phase
transition and show that, when the magnetic field is along the twin boundaries
(within about 2 degrees), the vortex solid is a Bose glass.
  Secondly, the effects of twins on the vortex dynamics are studied by
measuring the direction and magnitude of the total electric field while
rotating the current in the ab plane. We observe a partially guided vortex
motion along the dominating twin plane family, already apparent in the vortex
liquid, and becoming more and more pronounced as the temperature or the
magnetic field is reduced. There is no change related to the vortex phase
transition.
  Finally, the mixed state Hall effect is studied, with particular focus given
to the vortex phase transition. We show that the Hall resistivity scaling law
rho_xy=A*rho_xx^b remains unchanged in the vortex solid phase. For a magnetic
field along the twins, the exponent is b=2, corresponding to a constant Hall
conductivity. For a tilted magnetic field, we find b=1.4. In this case, the
Hall conductivity changes sharply at the vortex lattice melting, its slope
becoming much larger in the vortex solid. This effect is strongly current
dependent, and thus demonstrates that the Hall conductivity is pinning
dependent, hopefully solving a long term controversy. We also thoroughly review
the experimental data on the mixed state Hall effect, and discuss some
theoretical models concerning both the anomaly (a sign reversal of the Hall
effect) and the scaling law. A novel model for the Hall scaling law is given,
directly inspired from the theory of percolation in metallic conductors.
