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This study documents the preferred location and diurnal cycle of extreme convective storms that occur in the tropical band containing the east Pacific Ocean, Central and South America, the Atlantic Ocean, and northern Africa. Data from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar show three types of convective-stratiform structures that constitute extreme convective events: deep convective cores (DCCs), wide convective cores (WCCs), and broad stratiform regions (BSRs). Interim ECMWF ReAnalysis (ERA-Interim) data show the associated synoptic environmental factors associated with the occurrence of extreme convective features. The DCC, WCC, and BSR echoes are associated with early, middle, and late stages of convective system development, respectively, and the statistics and timing of their occurrence are related to topography and life cycle behavior of the convection. Storms containing DCC occur primarily over the Sudanian savannas of Africa and near the mountains in northern South America, being diurnally controlled. Storms with WCC manifest over land, in the same regions as the DCC, but also over oceanic regions. They appear around the clock but with maximum frequency at night. They are favored in regions of midlevel synoptic-scale low pressure systems, which over the sub-Sahara are the troughs of easterly waves. Storms containing BSR maximize over oceanic regions west of Africa and South America, where they exhibit a weak diurnal cycle with a slight midmorning maximum. Off the west coast of South America, the storms with WCC and BSR have longer lifetimes enhanced by orographic lifting over the Andes. The storms with BSR in the east Pacific Ocean often develop into tropical cyclones.