  Using steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze
relativistic outflows by means of examining the momentum equation along the
flow and in the transfield direction. We argue that the asymptotic Lorentz
factor is ~ mu-sigma_M, and the asymptotic value of the Poynting-to-matter
energy flux ratio - the so-called sigma function - is given by sigma/(1+sigma)
\~ sigma_M / mu, where sigma_M is the Michel's magnetization parameter and mu
c^2 the total energy-to-mass flux ratio. We discuss how these values depend on
the conditions near the origin of the flow. By employing self-similar solutions
we verify the above result, and show that a Poynting-dominated flow near the
source reaches equipartition between Poynting and matter energy fluxes, or even
becomes matter-dominated, depending on the value of sigma_M / mu.
