  The acceleration of relativistic jets from the Poynting to the matter
dominated stage is considered. The are generally two collimation regimes, which
we call equilibrium and non-equilibrium, correspondingly. In the first regime,
the jet is efficiently accelerated till the equipartition between the kinetic
and electro-magnetic energy. We show that after the equilibrium jet ceases to
be Poynting dominated, the ratio of the electro-magnetic to the kinetic energy
decreases only logarithmically so that such jets become truly matter dominated
only at extremely large distances. Non-equilibrium jets remain generally
Poynting dominated till the logarithmically large distances. In the only case
when a non-equilibrium jet is accelerated till the equipartition level, we
found that the flow is not continued to the infinity but is focused towards the
axis at a finite distance from the origin.
