Cargo operation can be decided into three basic categories:-
1. Fed Ex , UPS and DHL are primarily small package/box operators rather than bulk cargo.
These airlines use the large fleet to move small packages such as those distributed by Amazon , e-commerse, electronics and pharmaceuticals on a just in time basis and all do use HUBs.
Much/most of these kind of packages are ordered today and are required to be delivered tomorrow.
Goods get collected/dispatched from supplier depots all over the USA and indeed the world usually between 3 and 5 pm each working day are driven to local distribution hubs.
There they are sorted with local packages set aside for subsequent road delivery following morning, international and national packages are split and then these are loaded onto trucks for delivery to the nearest airport used by the said carrier .
Loaded onto planes and dispatched via various hubs transferred and flown to a distant point off loaded driven to another distribution depot . Loaded onto yet another truck and dispatched to the customers address.
This is logistics at work.
The aircraft used by these consolidators can be in house, franchised or contracted and frankly have nothing to do during the day .
2. Then you have the global true freight carriers Cathay Pacific Martinair Cargolux, Lufthansa Cargo, BA
World Cargo Korean etc.....
These tend to move bulk cargo and perishables from markets such as East Africa and Asia into Europe and North America and these are less likely to stand around during the day.
Their customers are direct sales , and freight forwarders and can be anything from a simple box through the cars/trucks and even other aircraft.
3. Thirdly you have ad-hoc charter and dedicated carriers such as Airbus and Evergreen special 744s and the An124/225
Hired on contract basis and operate as required.
That said they do tend to use off peak slots at the majors.