The potential change in precipitation due to global warming is studied using five-member ensembles of climate simulations by the CSIRO Mark 2 atmosphere-ocean model for the period 1871--1990 and forward to 2100 under both the Special Report on Emission Scenarios (SRES) A2 (rapid CO2 increase) and B2 (moderate increase) forcing scenarios. The mean surface warming for the period 1961--1990 is 0.3 K. The warming from 1961--1990 to 2071--2100 is 3.5 K under A2, 29% more than for B2, and with a very similar spatial pattern. The daily precipitation (P) frequency distributions for January and July days in these periods are presented, focusing on the A2 case. The distributions for wet days at each point are approximated by the gamma distribution. The global mean P increase of around 6%, in both months, is related to a mean increase in the gamma's scale parameter of 18%, offset by small decreases in the shape parameter and wet day frequency. However, local changes of opposite signs also occur, especially in the tropics. Ensemble averages of 30-year extreme daily precipitation for January and July, and other months, are generally greater for 2071--2100 than for 1961--1990, with an average increase of 14%. Extreme value theory based on the monthly gamma distributions provides a good match to these values. The theory is extended to the annual case. In general, the 1961--1990 extremes peak in the subtropical rainbands in the model, where increases of 10 to 30% are common. Larger relative increases occur in polar regions, and also over northern land in January.