We predict the structure and dynamics of disc galaxies using galaxy evolution models within a hierarchical formation scenario The halo mass aggregation histories, for a Lambda CDM model, were generated and used to calculate the virialization of dark matter (DM) haloes. A diversity of halo density profiles were obtained, the most typical one being close to the NFW profile. We modeled the formation of discs in centrifugal equilibrium within the evolving DM haloes using gas accretion rates proportional to the halo mass aggregation rates, and assuming detailed angular momentum conservation. We calculated the gravitational interactions between halo and disc, and the hydrodynamics, star formation, and evolution of the galaxy discs. We found that the slope and zero-point of the infrared Tully-Fisher relations (TFR) may be explained as a direct consequence of the cosmological initial conditions. This relation is almost independent of the assumed disc mass fraction. The rms scatter of the TFR originates mainly from the scatter in the DM halo structure and, to a minor extension, from the dispersion of the primordial spin parameter. The scatter obtained does not disagree with the observational estimates. Our models allow us to understand why the residuals of the TFR do not correlate significantly with disc size or surface brightness (SB), and why low and high SB galaxies have the same TFR. The correlations between gas fraction and SB, and between scale length and V_max agree with those observed. The discs present nearly exponential SB distributions. The shape of the rotation curves changes with the SB and is nearly flat for most cases. The rotation curve decompositions show a dominance of DM down to very small radii. The introduction of shallow cores in the DM halo attenuates this difficulty.
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