  Force-Free Electrodynamics (FFE) describes a particular regime of
magnetically dominated relativistic plasmas, which arises on several
astrophysical scenarios of interest such as pulsars or active galactic nuclei.
In this article, we present a full 3D numerical implementation of the FFE
evolution around a Kerr black hole. The novelty of our approach is
three-folded: i) We use the "multi-block" technique to represent a domain with
$S^2 \times \mathbb{R}^{+}$ topology within a stable finite-differences scheme.
ii) We employ as evolution equations those arising from a covariant
hyperbolization of the FFE system. iii) We implement stable and
constraint-preserving boundary conditions to represent an outer region given by
a uniform magnetic field aligned or misaligned respect to the symmetry axis.
  We find stationary jet solutions which reach equilibrium --through boundary
conditions-- with the outer numerical surface. This is so, even when the outer
boundary is located very close to the central region (i.e. $r_{out}\sim 10M $).
These numerical solutions reproduce most of the known results for analogue
astrophysical settings.
