An analytic model for a stationary force-free relativistic magnetized jet is presented. In those models a poloidal current provides the tension that balances the internal pressure. Our ignorance of the detailed conditions in the collimation zone is accounted for by specifying the current distribution as an (essentially free) function of the flux surfaces. The asymptotically cylindrical Grad-Schlüter-Shafranov (GSS) equation is solved for a nonlinear current distribution, I(Ψ) = c(1 – exp(−bΨ)) which covers both diffuse (b 《 1) and sharp (b 》 1) pinches, and weak (small c) and strong (large c) currents.