Porphyry copper deposits, the principal source of copper and molybdenum, form at convergent margins. Copper is precipitated from fluids associated with cooling magmas that have formed in the mantle and evolved at mid- to lower crustal levels, before rising toward the surface where they saturate and exsolve an aqueous fluid and copper. Despite advances in the understanding of their formation, there are still underexplored aspects of the genesis of porphyry copper deposits. Here we examine the role played by magma injection rates into the upper crust on the formation of porphyry copper deposits with different copper endowments. Mass balance calculations suggest that supergiant porphyry copper deposits (>10 million tonnes copper) require magma volumes (up to >2500 km ³ ) and magma injection rates (>0.001 km ³  year ⁻¹ ) typical of large volcanic eruptions from rift, hot spot, and subduction-related settings. Because large volcanic eruptions would destroy magmatic-hydrothermal systems or prevent their formation, the largest porphyry copper deposits can be considered as failed large eruptions and this may be one of the causes of their rarity.