  Relativistic, magnetized jets are observed to propagate to very large
distances in many Active Galactic Nuclei (AGN). We use 3D relativistic MHD
(RMHD) simulations to study the propagation of Poynting flux-driven jets in
AGN. These jets are assumed already being launched from the vicinity ($\sim
10^3$ gravitational radii) of supermassive black holes. Jet injections are
characterized by a model described in Li et al. (2006) and we follow the
propagation of these jets to ~ parsec scales. We find that these
current-carrying jets are always collimated and mildly relativistic. When
$\alpha$, the ratio of toroidal-to-poloidal magnetic flux injection, is large
the jet is subject to non-axisymmetric current-driven instabilities (CDI) which
lead to substantial dissipation and reduced jet speed. However, even with the
presence of instabilities, the jet is not disrupted and will continue to
propagate to large distances. We suggest that the relatively weak impact by the
instability is due to the nature of the instability being convective and the
fact that the jet magnetic fields are rapidly evolving on Alfv\'enic timescale.
We present the detailed jet properties and show that far from the jet launching
region, a substantial amount of magnetic energy has been transformed into
kinetic energy and thermal energy, producing a jet magnetization number $\sigma
< 1$. In addition, we have also studied the effects of a gas pressure supported
"disk" surrounding the injection region and qualitatively similar global jet
behaviors were observed. We stress that jet collimation, CDIs, and the
subsequent energy transitions are intrinsic features of current-carrying jets.
