We present N-body simulations of planetary system formation in thermally evolving, viscous disc models. The simulations incorporate type I migration (including corotation torques and their saturation), gap formation, type II migration, gas accretion on to planetary cores and gas disc dispersal through photoevaporation. The aim is to examine whether or not the oligarchic growth scenario, when combined with self-consistent disc models and up-to-date prescriptions for disc-driven migration, can produce planetary systems similar to those that have been observed. The results correlate with the initial disc mass. Low-mass discs form close-packed systems of terrestrial-mass planets and super-Earths. Higher mass discs form multiple generations of planets, with masses in the range 10 ≲ m p ≲ 45 M⊕. These planets generally type I migrate into the inner disc, because of corotation torque saturation, where they open gaps and type II migrate into the central star. Occasionally, a final generation of low- to intermediate-mass planets forms and survives due to gas disc dispersal. No surviving gas giants were formed in our simulations. Analysis shows that these planets can only survive migration if a core forms and experiences runaway gas accretion at orbital radii r ≳ 10 au prior to the onset of type II migration. We conclude that planet growth above masses m p ≳ 10 M⊕ during the gas disc lifetime leads to corotation torque saturation and rapid inward migration, preventing the formation and survival of gas giants. This result is in contrast to the success in forming gas giant planets displayed by some population synthesis models. This discrepancy arises, in part, because the type II migration prescription adopted in the population synthesis models causes too large a reduction in the migration speed when in the planet-dominated regime.