Abstract Epitaxial graphene growth was performed on the Si-terminated face of 4H-, 6H-, and 3C-SiC substrates by silicon sublimation from SiC in argon atmosphere at a temperature of 2000°C. Graphene surface morphology, thickness and band structure have been assessed by using atomic force microscopy, low-energy electron microscopy, and angle-resolved photoemission spectroscopy, respectively. Differences in the morphology of the graphene layers on different SiC polytypes is related mainly to the minimization of the terrace surface energy during the step bunching process. The uniformity of silicon sublimation is a decisive factor for obtaining large area homogenous graphene. It is also shown that a lower substrate surface roughness results in more uniform step bunching with a lower distribution of step heights and consequently better quality of the grown graphene. Large homogeneous areas of graphene monolayers (over 50×50μm2) have been grown on 3C-SiC (111) substrates. The comparison with the other polytypes suggests a similarity in the surface behaviour of 3C- and 6H-SiC.