Here is the short answer: A lead Component will be designated by the Decision Authority.  A MOA will be developed to further define roles and responsibilities. Ref: DODI 5000.85, Appendix 3C discusses Joint Programs. (See below for or click on DODI 5000.85 link for additional details)

Here is a link to the Joint Program Management Handbook.  Even though it is dated the processes/concepts haven't changed much and given our adaptive acquisition framework, it is a guide for Joint Program Management Programs.    https://www.acqnotes.com/Attachments/DAU%20Joint%20Program%20Management%20Handbook.pdf

---------------------------------------------

Joint Program Office Organization.

(1) A joint program office will be established when a defense acquisition program

involves the satisfaction of validated capability requirements from multiple DoD Components or

international partners, and is funded by more than one DoD Component or partner during any

phase of the acquisition process In joint programs, a lead Component will be designated to

manage the acquisition process and act as the acquisition agent for the participating DoD

Components. The participating DoD Components (i.e., those with a requirement for the

program’s products) support and participate with the lead DoD Component in managing the

acquisition process.

(2) Joint programs will be managed in accordance with the provisions of a memorandum

of agreement and with the lead DoD Component’s acquisition procedures and acquisition chain

of command, unless directed otherwise by the DAE.

(3) DoD Components will neither terminate nor substantially reduce participation in joint

MDAPs without capability requirements validation authority review and DAE approval. The

DAE may require a DoD Component to continue some or all funding, as necessary, to sustain the

joint program in an efficient manner, despite approving a request to terminate or reduce

participation. Memorandums of agreement between DoD Components should address

termination or reduced participation by any parties to the agreement. Substantial reduction will

be determined by the MDA in coordination with the requirements validation authority, and is

defined as a funding or quantity decrease that impacts the viability of the program or

significantly increases the costs to the other participants in the program

--------------------------------------------------------------------------------------------------