A comprehensive study on the step-controlled homoepitaxial growth on the (0001)Si-face of vicinal 4H–SiC substrates was performed in order to establish epitaxial growth on 2° towards 〈112¯0〉 off-cut substrates and 4° towards 〈11¯00〉 off-cut substrates. A standard epitaxial growth process was developed by optimizing the growth temperature T, Si/H ratio and C/Si ratio for growth on 4° towards 〈112¯0〉 off-cut substrates. Thereby, step-controlled epitaxial growth was achieved within a broad operating window. The surface roughness of such epilayers varies typically between rms=0.5nm and rms=2.5nm and step-controlled growth is conserved even at a growth rate of 27μm/h. Then, the standard growth process was applied to substrates with different off-cut angles α of 2°, 4° and 8° as well as with different off-cut directions 〈112¯0〉 and 〈11¯00〉. The step-controlled growth was achieved also within a wide range of Si/H ratio and C/Si ratio for growth on 8° and 4° off-cut substrates, but the process window narrows strongly for growth on 2° off-cut substrates. The epilayers' surface roughness increases with decreasing off-cut angle of the substrate. Epilayers grown on 4° towards 〈11¯00〉 off-cut substrates were significantly smoother than epilayers grown on 4° towards 〈112¯0〉 off-cut substrates. No influence of the substrates' off-cut angle and direction on the growth rate was found. The experimental results of this comprehensive study are discussed globally in consideration of other relevant publications.