When operational control changes what documentation is required to reflect this, a maintenance logbook entry?
ANSWER: When you speak of operational control, I am assuming that the aircraft is being operated by an FAR 135 or FAR 121 Air Carrier. If that were the case, the FAA would be notified through normal channels that an aircraft is being added or removed from the certificate.
There is no rule that requires a logbook entry be made. However, when an aircraft comes off lease, for example, and is transitioned to another carrier, we usually do make a record entry identifying the change in owner or operator. The main reason we make an entry is to accurately identify the aircraft total time and cycles at transition.
There is an advisory circular (AC) that speaks to the issue of operational control. It is AC 120-101. You can download a copy of that AC here.