It depends on the contract between the feeder and the 'mainline' carrier. Almost all, if not all, United Express work is done on a 'per departure' basis, meaning that the operating carrier receives a flat fee for each flight, no matter the load or route. UA
sets all fares (so uses the same yeild policies they use on all their other routes) and controls scheduling and routing.
On the other hand, Alaska and Horizon (which are seperate companies, despite being under the same holding co.), split the revenue. On all local O&D pax, QX
keeps all revenue, and on connecting pax (i.e. LAX
to Walla Walla), QX
receives a pro-rated share of the through fare. Similarly, QX
sets its own fares for local service, and AS
sets the through/connecting fares (this has changed recently as the AS
/QX pricing and yield depts have been merged, but same general concept still applies). Route planning and scheduling is done by QX
, but with heavy consultation between the two carriers.