All captains in our operation report directly to the Chief Pilot. Everyone else on board reports to the Captain, and certain on board, such as the ride-on mechanic, also report to the Director of maintenance.
If the Captain is out of his seat, or becomes incapacitated, the First Officer is in charge.
On long flights in which crewmembers require crew rest, an "augmented" or "heavy" crew will be on board. In an augmented crew, we have one first officer, two captains, and two flight engineers. A heavy crew has two first officer's also. When we fly augmented, the first officer only flies in the right seat. The captains take turns in both seats. When flying as a heavy crew, the first officers still only fly right seat, and the captains alternate through the left seat. We also utilize what's referred to as an "International Relief Pilot." This is similiar to a "cruise captain" position with other operators. The IRP can occupy either seat during cruise.
The concept of Operational Control is the guiding force in determining who can make what decisions. The Captain always has the ultimate authorityto act in the interest of safety of flight. However, the Captain holds joint operational control with the Director of Operations and the Dispatchers and Flight followers who initiate and monitor the flight as it progresses. A captain can certainly make a decision to divert. However, the company can also call and direct the captain to divert. The captain will then have the final say in determining if the divert can be done safely, and will accept or reject this action.
In a case where a diversion is necessary in the judgement of the captain, it's not a matter of calling to ask the company if it's okay. It's a matter of calling the company to advise them the captain has made a decision, and what his intentions are.
Operational Control is the authority to initiate, modify, or terminate or reject a flight. That belongs to the Director of Operations and those whom he delegates...and the Pilot in Command by his final authority with respect to the safe operation of the airplane, holds operational control jointly with the Director of Operations.
Practically speaking, the company is paying the paycheck. If the company wants something done and it can be done safely and legally, then it's going to get done the way the company wants.