The origin of the "deep boron related acceptor level" in SIC is subject to a lot of controversy. Based on ENDOR investigations, a B(Si)+V(C) model was suggested, while PL studies indicated the acceptor on the carbon sublattice. Our former ab initio LDA molecular cluster calculation showed that in the B(Si)+V(C) complex the carbon vacancy acts as the acceptor. Now, ah initio LDA supercell calculations have been carried out for boron-related complexes to calculate the occupation levels in 4H-SiC. It has been found that the 0/- level for the B(Si)+V(C) complex lies in the upper half of the gap, therefore it can be disregarded as the origin of the "deep boron-related acceptor level". Investigating other feasible boron-related complexes, B(Si)+Si(C) appears to be the best candidate.