Experiments of the 3-dimensional turbulent wall jet exhibit a rate of spread in the lateral direction significantly higher than that normal to the wall. The present contribution investigates the computed behaviour of the self-similar form of the jet, employing different levels of turbulence closure. It confirms that the rapid lateral spreading arises from the generation of streamwise vorticity, due to the anisotropy of the Reynolds stresses. However, even the best performing of the models tested overpredicts the spreading rate by some 50%. It is suggested that, because of the strong coupling between the axial and secondary flow, experiments require a significantly larger downstream distance to reach a fully-developed state than in the case of a 2-dimensional wall jet.