We investigate the effects of a variety of ingredients that must enter into a realistic model for disc galaxy formation, focusing primarily on the Tully–Fisher (TF) relation and its scatter in several wavebands. In particular, we employ analytic distributions for halo formation redshifts and halo spins, empirical star formation rates and initial mass functions, realistic stellar populations, and chemical evolution of the gas. Our main findings are as follows. (a) The slope, normalization and scatter of the TF relation across various wavebands are determined largely by the parent halo properties as dictated by the initial conditions, but are also influenced by star formation in the disc. (b) TF scatter in this model is due primarily to the spread in formation redshifts. The scatter can be measurably reduced by chemical evolution, and also by the weak anticorrelation between peak height and spin. (c) Multiwavelength constraints can be important in distinguishing between models that appear to fit the TF relation in I or K. (d) Assuming passive disc evolution, successful models seem to require that the bulk of disc formation cannot occur too early (z>2–3) or too late (z<0.2), and are inconsistent with high values of Ω₀. (e) A simple, realistic model with the above ingredients, and fewer free parameters than typical semi-analytic models, can reasonably reproduce the observed z=0 TF relation in all bands (B, R, I and K), as well as the observed B-band surface brightness–magnitude relation. In such a model, the near-infrared TF relation at z=1 is similar to that at z=0, while bluer bands show a markedly steeper TF slope at high redshift, consistent with limited current data. The remarkable agreement with observations suggests that the amount of gas that is expelled or poured into a disc galaxy may be small (though small fluctuations might serve to align B-band predictions better with observations), and that the specific angular momentum of the baryons should roughly equal that of the halo; there is little room for angular momentum transfer. In Appendix A we present analytic fits to stellar population synthesis models
