Abstract Porphyry Cu deposits range over five orders of magnitude in size (<0.01 to >100 Mt of contained Cu) despite common and reproducible ore-forming processes across continents and geologic times. The formation and size of these deposits are thought to be controlled by the optimal alignment of commonplace geologic, physical, and chemical processes. However, the relative weight of such processes in modulating the size of porphyry Cu deposits remains poorly quantified. Over the last few decades, new geologic and experimental data, analytical developments, and improved numerical models of deep and upper-crustal magmatic reservoirs have provided new insights into the chemical and physical evolution of transcrustal magmatic systems that lead to the formation of porphyry Cu deposits. Available data show that porphyry Cu deposits are formed by large volumes of hydrothermal fluids outgassed from a cyclically rejuvenated upper-crustal magma reservoir composed of intermediate to felsic magmas derived from the differentiation of primitive arc basalts in the lower crust. This transcrustal view of the magmatic system implies that physical and chemical processes taking place during (1) the generation of intermediate to felsic magmas in the lower crust, (2) their subsequent ascent, followed by (3) cooling, crystallization, fluid exsolution, and outgassing in the upper crust can strongly influence the size of the resulting porphyry deposits. Here we show that most chemical factors that affect the fertility of magmatic systems are preset during magmatic differentiation in the deep crust. Importantly, these chemical processes are not specific to porphyry-forming magmas but are in fact characteristic of intermediate arc magmas in general. Within geologically permissible ranges, the chemical fertility of arc magmas can modulate the size of porphyry Cu deposits within one order of magnitude, insufficient to explain the full range of Cu endowment observed in these deposits. In contrast, physical aspects such as the lifetime (i.e., the combined duration of magma accumulation and crystallization) and volume of an effective magma body appear to be the major controls on the size of porphyry Cu deposits. The efficiency of the magmatic system refers to its ability to outgas fluids in a focused manner and yet avoid a catastrophic explosive volcanic eruption during incremental growth of the system through successive magma recharges. The intrusive magma flux, thermal gradient, and rheological state of the intruded crust all appear to be the major factors that influence the formation and size of the effective magma body, and thus, the formation and size of porphyry Cu deposits. We highlight the role of long-lived transcrustal arc maturation in developing this physical fertility and argue that the understanding of magmatic systems associated with porphyry deposits from a physical point of view will be the key to the definition of new exploration guidelines for giant porphyry Cu deposits.