  Relativistic magnetized jets are key elements in Active Galactic Nuclei and
in other astrophysical environments. Their structure and evolution involves a
complex nonlinear physics that can be approached by numerical studies only.
Still, owing to a number of challenging computational aspects, only a few
numerical investigations have been undertaken so far. In this paper, we present
high-resolution three dimensional numerical simulations of relativistic
magnetized jets carrying an initially toroidal magnetic field. The presence of
a substantial toroidal component of the field is nowadays commonly invoked and
held responsible for the process of jet acceleration and collimation. We find
that the typical nose cone structures, commonly observed in axisymmetric
two-dimensional simulations, are not produced in the 3D case. Rather, the
toroidal field gives rise to strong current driven kink instabilities leading
to jet wiggling. However, it appears to be able to maintain an highly
relativistic spine along its full length. By comparing low and high resolution
simulations, we emphasize the impact of resolution on the jet dynamical
properties.
