General activator of RNA polymerase III transcription. Interacts with TBP. Binds to Pol III subunit C34 and to the TAU135 component of TFIIIC. TFIIIB comprises the TATA-binding protein (TBP), the B-related factor (BRF) and the B' component (TFC5). Present with 4330 molecules/cell in log phase SD medium. Belongs to the TFIIB family.