Laser driven accelerators are capable of producing multi nC, multi MeV electron beams with transverse and longitudinal sizes on the order of microns. To investigate the transport of such electron bunches, a fast and fully relativistic space charge code which can handle beams with arbitrarily large energy spread has been developed. A 6-D macroparticle model for the beam is used to calculate the space charge fields at each time step. The collection of macroparticles is divided into longitudinal momentum bins, each with a small spread in relative momentum. The macroparticle distribution in each momentum bin is decomposed into ellipsoidal shells in position space. For each shell, an analytical expression for the electrostatic force in the bin rest frame is used. The total space charge force acting on one macroparticle in the lab frame is then the vector sum of the Lorentz-transformed forces from all the momentum bins. We have used this code to study the evolution of typical beams emerging from the plasma in the two most popular schemes, i.e., the self-modulated laser-wakefield-accelerator, where the laser pulse size is many times the plasma wavelength (L >> lr), and the colliding pulse laser-wakefield-accelerator regime where L ~; lr and two counter propagating laser pulses are used to inject electrons into the wakefield.