We quantify the systematics in the size-luminosity relation of galaxies in the SDSS main sample which arise from fitting different 1- and 2-component model profiles to the images. In objects brighter than L*, fitting a single Sersic profile to what is really a two-component SerExp system leads to biases: the half-light radius is increasingly overestimated as n of the fitted single component increases; it is also overestimated at B/T ~ 0.6. However, the net effect on the R-L relation is small, except for the most luminous tail, where it curves upwards towards larger sizes. We also study how this relation depends on morphological type. Our analysis is one of the first to use Bayesian-classifier derived weights, rather than hard cuts, to define morphology. Crudely, there appear to be only two relations: one for early-types (Es, S0s and Sas) and another for late-types (Sbs and Scds). However, closer inspection shows that within the early-type sample S0s tend to be 15% smaller than Es of the same luminosity, and, among faint late types, Sbs are more than 25% smaller than Scds. Neither the early- nor the late-type relations are pure power-laws: both show significant curvature, which we quantify. However, the R-L relations of the bulges of early-types are almost pure power laws. Our analysis confirms that two mass scales are special for early-type galaxies: M* = 3e10 and 2e11 Msun. These same mass scales are also special for late types: there is almost no correlation between R and M* below the former, and almost no late-types above the latter. We also show that the intrinsic scatter around the relation decreases at large luminosity and/or stellar mass; this should provide additional constraints on models of how the most massive galaxies formed.
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