  Astrophysical jets, launched from the immediate vicinity of accreting black
holes, carry away large amounts of power in a form of bulk kinetic energy of
jet particles and electromagnetic flux. Here we consider a simple analytical
model for relativistic jets at larger distances from their launching sites,
assuming a cylindrical axisymmetric geometry with a radial velocity shear, and
purely toroidal magnetic field. We argue that, as long as the jet plasma is in
magnetohydrostatic equilibrium, such outflows tend to be particle dominated,
i.e. the ratio of the electromagnetic to particle energy flux, integrated over
the jet cross-sectional area, is typically below unity, $\sigma < 1$. At the
same time, for particular magnetic and radial velocity profiles, magnetic
pressure may still dominate over particle pressure for certain ranges of the
jet radius, i.e. the local jet plasma parameter $\beta_{pl} < 1$, and this may
be relevant in the context of particle acceleration and production of
high-energy emission in such systems. The jet magnetization parameter can be
elevated up to the modest values $\sigma \lesssim \mathcal{O}(10)$ only in the
case of extreme gradients or discontinuities in the gaseous pressure, and a
significantly suppressed velocity shear. Such configurations, which consist of
a narrow, unmagnetized jet spine surrounded by an extended, force-free layer,
may require an additional poloidal field component to stabilize them against
current-driven oscillations, but even this will not elevate substantially their
$\sigma$ parameter.
