With the very high electron cyclotron (EC) wave power density achieved in the TCV tokamak, more than 20 MW m(-3), quasilinear modelling predicts an electron cyclotron current drive (ECCD) efficiency well in excess to the experimental value, by up to a factor of 10. Experimentally, radial transport of suprathermal electrons consistent with a diffusion coefficient larger than 1.5 m(2) s(-1) has been observed. This implies that the radial transport time is of the same order as the electron deflection time, suggesting that the key to resolving the discrepancy is to include radial transport in the kinetic simulations. In this paper we show that with a diffusion coefficient in accordance with the experimental estimation, we can reproduce the observed current drive efficiency in the fully EC current driven plasmas of TCV by solving the Fokker-Planck equation. Experimentally the total wave-driven current is well-known since the current in the Ohmic transformer is set to a constant value. We study the radial profile and the velocity dependence of the radial diffusion coefficient. A specific model is employed for steady-state electron internal transport barriers, produced by off-axis ECCD, with the electrons divided into two groups according to their energy. A small diffusion coefficient is assigned for the low-energy electrons, while at higher energies the diffusion level is chosen such as to obtain the experimental ECCD efficiency. The total current density, which is the sum of the wave-driven part and the bootstrap current, is found to be hollow, supporting the hypothesis that the reversed shear is the cause of the transport barrier.