What typically happens when two or more professors from the same department want the same prospective PhD student? If a talented PhD applicant names (in their statement of purpose) two or three professors at a department that they'd like to work with, and this student is accepted by the department, with all of the named professors equally desiring to hire this student into their respective research groups, then what lands up happening, typically?

A coin toss?

Give the student to an academically younger prof.?
I think that you would ultimately have the final choice in the matter. The supervisor is somebody that you have to work with for 4+ years, so you better make sure you choose the one you think you can handle for that period of time.