Given the threats from rainstorm events that have been intensified due to climate change, the investigation of heavy/extreme precipitation is attracting increasing attention. The investigation of extreme precipitation, with its restricted tools and data, is quite different from that of nonextreme precipitation. Satellite precipitation estimates (SPEs) are promising precipitation measurements due to fine spatial resolution. However, the spatiotemporal patterns of SPE extremes remain unclear. Therefore, this study attempted to systematically analyse the spatiotemporal patterns of extreme SPEs provided by the Tropical Rainfall Measurement Mission (TRMM) research product from statistical characterization to stochastic behaviour modelling. The statistical characterization was depicted using comprehensive extreme precipitation indices (EPIs), while the stochastic behaviour was modelled using the generalized Pareto distribution (GPD) to fit the 'peak over threshold' samples and employing the max-stable process to fit the 'block maximum' samples (Max: annual 1-day maximum, RX1day: monthly 1-day maximum, and RX5day: monthly 5-day maximum) of the TRMM data. The TRMM extremes were analysed across the Xijiang River Basin, China. The results of the statistical