From my understanding, the larger unit is always the exercitus. For example, if the Legatus Augusti pro Praetore Moesiae had to sent a detachement in order to support Trajans campaign starting in Syria he sent some legionary cohorts from his legions, plus some auxilia cohorts and alae. These are all full units of cohort size from my understanding. If all these units marched together to Syria under one vexillum or not is unknown as far as I know.
Well, there was also the case, that e.g. a detachement of the size of 2 cohorts from a legion was established via collecting 1000 men from all 10 cohorts of a legion. Or all alae of the exercitus contributed a few turmae, which were in total then a unit of ala size. At least there is a theory about it.
Size does not matter. Even if during late empire the units were smaller. A detachement is a detachment. Regardless if 5 men or 2000 men. Well, there was obviously a point in time, when the romans did not call a detachment vexillatio anymore. But that does not mean, that they stopped working with detachments. At least detachements from the duces directly onsite, where the campaign happens.
Of course the military strategy of the late empire with regional and central field armies was different than in the 2nd century. Limitanei were supposed to stay were they are and not move to the other end of the world. So I cannot believe, that a Dux Moesia had to contribute units to Julians campaign in Mesopotamia, like the Legatus Moesiae did in Trajans time. But the Duces of the eastern front (Syriae, Mesopotamia, Osroene, Palaestinae, ...) should have reenforced his campaigning army onsite.
Well, there was also the case, that e.g. a detachement of the size of 2 cohorts from a legion was established via collecting 1000 men from all 10 cohorts of a legion. Or all alae of the exercitus contributed a few turmae, which were in total then a unit of ala size. At least there is a theory about it.
Size does not matter. Even if during late empire the units were smaller. A detachement is a detachment. Regardless if 5 men or 2000 men. Well, there was obviously a point in time, when the romans did not call a detachment vexillatio anymore. But that does not mean, that they stopped working with detachments. At least detachements from the duces directly onsite, where the campaign happens.
Of course the military strategy of the late empire with regional and central field armies was different than in the 2nd century. Limitanei were supposed to stay were they are and not move to the other end of the world. So I cannot believe, that a Dux Moesia had to contribute units to Julians campaign in Mesopotamia, like the Legatus Moesiae did in Trajans time. But the Duces of the eastern front (Syriae, Mesopotamia, Osroene, Palaestinae, ...) should have reenforced his campaigning army onsite.
Ut desint vires, tamen est laudanda voluntas