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Abstract 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, σ < 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 β 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 of σ ≲  ( 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 substantially elevate their σ parameter.