  This work presents the first characterization of the internal structure of
overpressured steady superfast magnetosonic relativistic jets in connection
with their dominant type of energy. To this aim, relativistic
magnetohydrodynamic simulations of different jet models threaded by a helical
magnetic field have been analyzed covering a wide region in the magnetosonic
Mach number - specific internal energy plane. The merit of this plane is that
models dominated by different types of energy (internal energy: hot jets;
rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux
dominated jets) occupy well separated regions. The analyzed models also cover a
wide range of magnetizations. Models dominated by the internal energy (i.e.,
hot models, or Poynting-flux dominated jets with magnetizations larger than but
close to 1) have a rich internal structure characterized by a series of
recollimation shocks and present the largest variations in the flow Lorentz
factor (and internal energy density). Conversely, in kinetically dominated
models there is not much internal nor magnetic energy to be converted into
kinetic one and the jets are featureless, with small variations in the flow
Lorentz factor. The presence of a significant toroidal magnetic field threading
the jet produces large gradients in the transversal profile of the internal
energy density. Poynting-flux dominated models with high magnetization (>10)
are prone to be unstable against magnetic pinch modes, which sets limits to the
expected magnetization in parsec-scale AGN jets {and/or constrains their
magnetic field configuration}.
