Motivated by the wide range of projections of regional rainfall (or precipitation, pr) based on the CMIP5 ensemble of global climate models, we investigate the atmospheric moisture budget of idealized rising-CO 2 (1pctCO2) simulations from 10 models submitted to CMIP6. We use the new CMIP6 standard variables, the vertically integrated eastward and northward moisture flux, and provide a multi-model assessment of these, their convergence (conv), along with water vapour path (prw). Seasonal climatologies of a 20-year base climate for pr, prw, flux, and conv match well those from the ECMWF's Reanalysis 5. In addition, composites 'H' of quantities for months in the top decile of monthly rainfall, calculated at each model grid point, produce a field of heavy rainfall, on average double that of the mean. Spatial correlation coefficients (r) between the pr and conv fields are typically .7 in each season. This rises to .9 for the corresponding H fields, due to the important link between moisture convergence and heavy rainfall. Fields of standardized change (Δ), or change per degree of global warming, were calculated. The ensemble-mean Δpr is only weakly correlated with the base climate pr, and likewise for conv. However, the prw change is highly correlated with the base prw, pointing to the importance of the "thermodynamic" change in that variable. Globally, the net Δconv is highly correlated with Δpr, around .9. This rises to .95 for the heavy-rain composites. Relationships between changes in pr and other components hold at grid points also, when the individual model results are correlated. Clearly, there is a dependence in the change in pr with that in conv, particularly for heavy rainfall. Assessment of a larger ensemble from CMIP6, using the new flux variables, would improve the evaluation of these processes, and potentially allow more confident projections in future rainfall changes.