Images from the Hubble Space Telescope Advanced Camera for surveys are used to carry out a new photometric study of the globular clusters (GCs) in M104, the Sombrero galaxy. The primary focus of our study is the characteristic distribution function of linear sizes [size distribution function (SDF)[ of the GCs. We measure the effective radii for 652 clusters with point spread function-convolved King and Wilson dynamical model fits. The SDF is remarkably similar to those measured for other large galaxies of all types, adding strong support to the view that it is a 'universal' feature of GC systems. We use the Sombrero and Milky Way data and the formation models of Baumgardt & Kroupa (2007) to develop a more general interpretation of the SDF for GCs. We propose that the shape of the SDF that we see today for GCs is strongly influenced by the early rapid mass loss during their star-forming stage, coupled with stochastic differences from cluster to cluster in the star formation efficiency (SFE) and their initial sizes. We find that the observed SDF shape can be accurately predicted by a simple model in which the protocluster clouds had characteristic sizes of 0.9 ± 0.1 pc and SFEs of 0.3 ± 0.07. The colours and luminosities of the M104 clusters show the clearly defined classic bimodal form. The blue sequence exhibits a mass/metallicity relation, following a scaling of heavy-element abundance with luminosity of Z ∼ L0.3 very similar to what has been found in most giant elliptical galaxies. A quantitative self-enrichment model provides a good first-order match to the data for the same initial SFE and protocluster size that were required to explain the SDF. We also discuss various forms of the GC Fundamental Plane of structural parameters and show that useful tests of it can be extended to galaxies beyond the Local Group. The M104 clusters strongly resemble those of the Milky Way and other nearby systems in terms of such test quantities as integrated surface density and binding energy.