"Hanzei"means that the Muromachi bakufu (Japanese feudal government headed by a shogun) gave the power of collection of half of the customs or taxes on production from manors and lands under the control of the feudal government to the provincial constables.
半済（はんぜい）は、室町幕府が荘園・公領の年貢半分の徴収権を守護に認めたことを指す。