High-capacity extrusion die assemblies (20, 90, 130, 140, 180, 252) each having a tubular section (44, 146, 162, 268) and an elongated, axially rotatable, helically flighted screw section (56, 56a, 152, 168, 276, 278) which cooperatively define frustoconical, outwardly diverging material flow paths (75, 160, 291) at constant or differing divergence angles of from about 1-11°. The use of diverging tubular sections (44, 146, 162, 268) and screw sections (56, 56a, 152, 168, 276, 278) permits the use of larger die plates (76, 118, 292) with an increased number of die openings (80, 124, 296). This allows significant increases in extrusion production rates. The die assemblies (20, 90, 130, 140, 180, 252) can be used in the production of a wide number of human foods or animal feeds, and particularly aquatic feeds of the floating or sinking variety. In another aspect of the invention, an extruder (210) is provided having diverging and converging sections (212, 214) along the length thereof and defining corresponding flow paths (230, 246).