Substrate-specific adapter of a BCR (BTB-CUL3-RBX1) E3 ubiquitin-protein ligase complex involved in regulation of cytoskeleton structure. The BCR(TNFAIP1) E3 ubiquitin ligase complex mediates the ubiquitination of RHOA, leading to its degradation by the proteasome, thereby regulating the actin cytoskeleton and cell migration. Its interaction with RHOB may regulate apoptosis. May enhance the PCNA- dependent DNA polymerase delta activity. {ECO:0000269|PubMed:19637314, ECO:0000269|PubMed:19782033}. This is the function of ENSG00000109079 (TNFAIP1, TNF alpha induced protein 1).