What command relationship implies that units are placed in an organization for a relatively permanent duration?

The command relationship referred to in the context of units being placed in an organization for a relatively permanent duration is indeed assignment. When a unit is assigned, it is given a specific, long-term role or mission within a higher headquarters, indicating a stable and consistent relationship. This means that the assigned units can expect to operate under the command structure and priorities of the gaining unit for an extended period, allowing for better integration and unity of effort.

In contrast, organic units refer to those that belong to a particular parent organization and are inherently a part of that unit's structure. Operational control implies a more temporary or task-specific command relationship, allowing for the movement of units for particular operations without long-term commitment. Task organization denotes the temporary grouping of units or personnel for a specific mission or task, which also does not imply permanence. Therefore, assignment appropriately captures the essence of a more stable command relationship.