The patentee carries it out by himself.
Patent profits belong to the patentee. For example, C produces its own patented products, and all the proceeds go to C.
The patentee permits others to carry out it.
All three patentees have the right to license the production of others. For example, if C gives Z a general patent license, the royalties paid by Z should be equally distributed among A, B and C ... unless there is an agreement.
Based on the above two points, the third inventor can cooperate with others on the patent, but only need to pay the patent fees of other inventors.
Inconsistencies between the inventor and the applicant:
If the invention is a service invention, then the patentee is the company where the inventor works, and the third inventor is not allowed to cooperate with others without authorization.