Electron transport and current profiles through gated graphene ribbons are addressed within the tight-binding Keldysh formalism. Conductance, conductivity, and current quantum shot noise are studied numerically as functions of the width of the ribbons, length of the gated region, and strength of the gate potential. Crossover between pseudodiffusive and ballistic transport regimes is examined in detail. In particular, around the energy of the gate potential, it is shown that the pseudodiffusive regime occurs even for moderate potential strengths, well below the onset of the sp2 hybridized bands of graphene. These findings are supported by the evaluation of current profiles of the massless Dirac fermions throughout graphene ribbons.