  We perform full 3D numerical simulations of compact objects, such as black
holes or neutron stars, boosted through an ambient force-free plasma that
posses a uniform magnetization. We study jet formation and energy extraction
from the resulting stationary late time solutions.The implementation of
appropriate boundary conditions has allowed us to explore a wide range of boost
velocities, finding the jet power scales as $\gamma v^2$ (being $\gamma$ the
Lorentz factor). We also explore other parameters of the problem like the
orientation of the motion respect to the asymptotic magnetic field or the
inclusion of black hole spin. Additionally, by comparing a black hole with a
perfectly conducting sphere in flat spacetime, we manage to disentangle
curvature effects from those produced by the perfect conducting surface. It is
shown that when the stellar compactness is increased these two effects act in
combination, further enhancing the luminosity produced by the neutron star.
