An apparatus for dispensing a roll of material with one hand is disclosed that includes a shaft having a core segment for supporting a roll of material and a handle segment that is integral with the core segment. The handle segment has an annular recess with a collar received therein. The apparatus includes a gripper received over the handle segment of the shaft. The gripper has a cylindrically shaped body defining an open center that has an open upper end and a closed lower end. The gripper is positioned on the handle segment with its open upper end between the collar and the core segment. The shaft is rotatable relative to the gripper and the gripper is hand-compressible to bring the gripper into frictional contact with the shaft to slow or stop the rotation of the shaft.