From what I know there are never two aircraft with the same registration even if the aircraft isn't flying anymore. But there is a F-27 in the db with reg. N737A. There is a Boeing 737-7AX BBJ s/n 30181 with this registration right now. Both are/were owned by Aramco. Can they keep one registration and apply it to a different aircraft or what? How is it done?
Yes, you are correct in saying that no aircraft can carry the same registration at any time. But it is possible however for older aircraft that are not airworthy to have been deleted from the register but still have the old registration applied to the aircraft.
This has been done with quite a few Icelandic airplanes.
For example, two Air Atlanta jets have had the registration TF-ABQ (not at the same time, of course). The former one was a 747-128 and the latter a 747-246B. For more information on these two, look at these pages:
QANTAS has done this with a number of aircraft.
They recycled the VH-ECA/VH-EBA etc regos from
the 707s to the 747s. What has always puzzled
me is how the aircraft manufacturers will assign the
same test registration over and over again. Look at
Boeing or Airbus. You see the same registration
used probably 50 times or more...