  In relativistic, Poynting dominated outflows, acceleration and collimation
are intimately connected. An important point is that the Lorentz force is
nearly compensated by the electric force therefore the acceleration zone spans
a large range of scales. We derived the asymptotic equations describing
relativistic, axisymmetric MHD flows far beyond the light cylinder. These
equations do not contain either intrinsic small scales (like the light cylinder
radius) or terms that nearly cancel each other (like the electric and magnetic
forces) therefore they could be easily solved numerically. They also suit well
for qualitative analysis of the flow and in many cases, they could even be
solved analytically or semi-analytically. We show that there are generally two
collimation regimes. In the first regime, the residual of the hoop stress and
the electric force is counterbalanced by the pressure of the poloidal magnetic
field so that at any distance from the source, the structure of the flow is the
same as the structure of an appropriate cylindrical equilibrium configuration.
In the second regime, the pressure of the poloidal magnetic field is negligible
small so that the flow could be conceived as composed from coaxial shrinking
magnetic loops. In the two collimation regimes, the flow is accelerated in
different ways. We study in detail the structure of jets confined by the
external pressure with a power law profile. In particular, we obtained simple
scalings for the extent of the acceleration zone, for the terminal Lorentz
factor and for the collimation angle.
