We present the first detailed comparative study of the adsorption and thermal processing of the three astrophysically important C2O2H4 isomers glycolaldehyde, methyl formate, and acetic acid adsorbed on a graphitic grain analogue at 20 K. The ability of the individual molecule to form intermolecular hydrogen bonds is extremely important, dictating the growth modes of the ice on the surface and the measured desorption energies. Methyl formate forms only weak intermolecular bonds and hence wets the graphite surface, forming monolayer, bilayer, and multilayer ices, with the multilayer having a desorption energy of 35 kJ mol(-1). In contrast, glycolaldehyde and acetic acid dewet the surface, forming clusters even at the very lowest coverages. The strength of the intermolecular hydrogen bonding for glycolaldehyde and acetic acid is reflected in their desorption energies (46.8 and SS kJ mol(-1), respectively), which are comparable to those measured for other hydrogen-bonded species such as water. Infrared spectra show that all three isomers undergo structural changes as a result of thermal processing. In the case of acetic acid and glycolaldehyde, this can be assigned to the formation of well-ordered, crystalline, structures where the molecules form chains of hydrogen-bonded moieties. The data reported here are of relevance to astrochemical studies of hot cores and star-forming regions and can be used to model desorption from interstellar ices during the warm up phase with particular importance for complex organic molecules.