We analyse the effects of substrate polishing and of the epilayer thickness on the quality of graphene layers grown by high temperature annealing on 3C–SiC(111)/Si(111) by scanning tunnelling microscopy, x-ray photoelectron spectroscopy, Raman spectroscopy, low energy electron diffraction and high resolution angle resolved photoemission spectroscopy. The results provide a comprehensive set of data confirming the superior quality of the graphene layers obtained on polished substrates, and the limitations of the growth obtained on unpolished surfaces.