you are right, there is very little choice for an operator as to where and how to apply the registration to its aircraft. Apart from the registration's location, the rules generally also outline fontstyle, size, contrast and other legibility concerns. Similar rules also exist on how and where an aircraft is to carry the flag of its registration state.
While ICAO ensures that its member states comply with certain minimum standards regarding registration rules, quite a few national pecularities remain. Among the things left to the individual national lawmakers you find questions such as:
- Whether a registration - apart from the country code - is numeric (e.g. China), alphanumeric (e.g. US) or alphabetical (e.g. France).
- Whether registrations are assigned strictly in chronological order (e.g. Spain), or according to the bearer's wishes on a first come, first serve basis (e.g. UK), or following a strict logic portraying additional information with e.g. the first letter indicating the weight class of the aircraft (e.g. Germany - ever wondered why registrations on all of Lufthansa's & its competitors' jets start with the letters D-Axxx ?).
- Whether a registration can be re-assigned to a different airframe after the original bearer of said registration has been decommissioned (e.g. Canada), whether it can only be re-assigned to the very same airframe should it be re-imported at a later stage (e.g. Switzerland), or whether it cannot be re-issued at all once it has been cancelled (e.g. Spain).
- Whether all aircraft need to display the flag and nationality marks (common), or whether aircraft never leaving the registration state can be exempt from that (e.g. General Aviation aircraft and helicopters in New Zealand that rarely display the ZK
- in their markings, just the three letters of the actual registration).
And so on... Cheers, Lukas