  We study relativistic magnetized outflows using relativistic equation of
state having variable adiabatic index ($\Gamma$) and composition parameter
$(\xi)$. We study the outflow in special relativistic magneto-hydrodynamic
regime, from sub-Alfv\'enic to super-fast domain. We showed that, after the
solution crosses the fast point, magnetic field collimates the flow and may
form a collimation-shock due to magnetic field pinching/squeezing. Such fast,
collimated outflows may be considered as astrophysical jets. Depending on
parameters, the terminal Lorentz factors of an electron-proton outflow can
comfortably exceed few tens. We showed that due to the transfer of angular
momentum from the field to the matter, the azimuthal velocity of the outflow
may flip sign. We also study the effect of composition $(\xi)$ on such
magnetized outflows. We showed that relativistic outflows are affected by the
location of the Alfv\'en point, the polar angle at the Alfv\'en point and also
the angle subtended by the field lines with the equatorial plane, but also on
the composition of the flow. The pair dominated flow experiences impressive
acceleration and is hotter than electron proton flow.
