This paper reports the synthesis and detailed characterization of graphite thin films produced by thermal decomposition of the (0001) face of a 6H-SiC wafer, demonstrating the successful growth of single crystalline films down to approximately one graphene layer. The growth and characterization were carried out in ultrahigh vacuum (UHV) conditions. The growth process and sample quality were monitored by low-energy electron diffraction, and the thickness of the sample was determined by core level x-ray photoelectron spectroscopy. High-resolution angle-resolved photoemission spectroscopy shows constant energy map patterns, which are very sharp and fully momentum-resolved, but nonetheless not resolution limited. We discuss the implications of this observation in connection with scanning electron microscopy data, as well as with previous studies.