Step 1: The trick with Mapleson systems is to match the geometry of the bag, fresh-gas inlet and pop-off valve to the ventilation mode that wastes the least fresh gas.
Step 2: In the Magill (Mapleson A) layout the relief valve sits near the patient. While a patient breathes on his own, the early expirate (anatomical dead-space, which is fresh) is retained in the tubing and reused, and only the later CO2-rich alveolar gas escapes through the valve. The result is no significant rebreathing at a fresh gas flow about equal to alveolar minute ventilation.
Step 3: Because of this economy, Mapleson A is the circuit of choice for spontaneous ventilation. By contrast, Mapleson D wins for controlled ventilation, while B and C are inefficient and demand high flows in either mode.
\[\boxed{\text{Mapleson A}}\]