Paper is unwound from the inside diameter of a tubular roll of paper in a dispensing container, is threaded downwardly through a dispensing funnel installed in a hole in the bottom wall of the container, and is adapted to be pulled downwardly from the funnel and torn into individual hand wipers. The funnel is formed with three dispensing ports of different sizes to accommodate paper of different thicknesses and includes an angled lower end portion which promotes reliable tearing of the paper and causes a tail of predetermined length to be left extending from the funnel for use in the next dispensing operation. The angled lower end portion of the funnel may be pointed forwardly if the dispenser is mounted at a relatively high elevation and may be pointed rearwardly if the dispenser is mounted at a relatively low location. The funnel may be installed securely in holes of different diameters and used with bottom walls of different thicknesses.