We present a comprehensive analysis of the morphology and dynamics of relativistic pressure-matched axisymmetric jets. The numerical simulations have been carried out with a high-resolution shock-capturing hydro-code based on an aprpoximate relativistic Riemann solver derived form the spectral decomposition of the Jacobian matrices of relativistic hydrodynamics. We discuss the dependence of the jet morphology on several parameters paying special attention to the relativistic effects caused by high Lorentz factors and large internal energies of the beam flow. The parameter space of our analysis is spanned by the ratio of the beam and ambient medium rest mass density (#eta#), the beam Mach number (M_b), the beam Lorentz factor (W_b) and the a...