From two very simple axioms: (1) that active galactic nucleus activity traces spheroid formation, and (2) that the cosmic star formation history is dominated by spheroid formation at high redshift, we derive simple expressions for the star formation histories of spheroids and discs, and their implied metal enrichment histories. Adopting a Baldry-Glazebrook initial mass function we use these relations and apply PEGASE.2 to predict the z = 0 cosmic spectral energy distributions (CSEDs) of spheroids and discs. The model predictions compare favourably to the dust-corrected CSED recently reported by the Galaxy And Mass Assembly team from the far-ultraviolet through to the K band. The model also provides a reasonable fit to the total stellar mass contained within spheroid and disc structures as recently reported by the Millennium Galaxy Catalogue team. Three interesting inferences can be made following our axioms: (1) there is a transition redshift at z ≈ 1.7 at which point the Universe switches from what we refer to as 'hot mode evolution's (i.e. spheroid formation/growth via mergers and/or collapse) to what we term 'cold mode evolution' (i.e. disc formation/growth via gas infall and minor mergers); (2) there is little or no need for any pre-enrichment prior to the main phase of star formation; (3) in the present Universe mass loss is fairly evenly balanced with star formation holding the integrated stellar mass density close to a constant value. The model provides a simple prediction of the energy output from spheroid and disc projenitors, the build-up of spheroid and disc mass and the mean metallicity enrichment of the Universe. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.