  In this paper, we investigate the acceleration in relativistic jets of
high-energy proton preaccelerated in the magnetosphere of a supermassive black
hole. The proton reaches maximum energy when passing the total potential
difference of $U$ between the jet axis and its periphery. This voltage is
created by a rotating black hole and transmitted along magnetic field lines
into the jet. It is shown that the trajectories of proton in the jet are
divided into three groups: untrapped, trapped and not accelerated. Untrapped
particles are not kept by poloidal and toroidal magnetic fields inside the jet,
so they escape out the jet and their energy is equal to the maximum value,
$eU$. Trapped protons are moving along the jet with oscillations in the radial
direction. Their energy varies around the value of $0.74 eU$. In a strong
magnetic field protons preaccelerated in the magnetosphere are pressed to the
jet axis and practically are not accelerated in the jet. The work defines
acceleration regimes for a range of the most well-known AGN objects with
relativistic jets and for the microquasar SS433.
