The shallow boron acceptors in 3C-, 4H-and 6H-SiC were investigated with electron paramagnetic resonance (EPR) at high frequency (142 GHz) providing a precise knowledge of the electronic g tensors. The hyperfine (hf) interactions of the boron acceptor on the hexagonal site and the quasi-cubic site in 4H-SiC were determined precisely with electron nuclear double resonance (ENDOR). The 11 B hf interactions and superhyperfine (shf) interactions with surrounding 29 Si and 13 C neighbours were interpreted within a semiempirical analysis. The microscopic model suggested from the EPR and ENDOR results and from the semiempirical analysis is as follows: the shallow boron acceptors have the same electronic structure in 6H-, 4H-and 3C-SiC and have to be viewed as B-induced C acceptors. The hole is located in the connection line between B Si and the adjacent C. Depending on the microwave frequency used in the measurements the hole at the quasi-cubic site defects experiences a thermally activated motion about the hexagonal crystal axis at high temperatures.