Maybe the reason tha you're not getting many answers is that your question is rather difficult to answer without assuming that you understand the international aviation industry. What you want to know is normally learned - and is background knowledge that is used in response to a particular context - during several years of training and another few putting the training into practise.
Don't make too many assumptions about how correct this is because one needs far more information to offer a professional opinion but here are a few pointers.
- As I recall, as far as you appear to need to understand it, all airspace is the responsibility of one State - regardless of how far offshore the aircraft may be.
- All airspace is classified from the range A through G. The classification determines what can go on in the airspace and under what circumstances (including crew qualifications, aircraft fit and comms etc.).
- Aircraft are registered in one State and (assuming the the State of registration is a signatory to the ICAO convention) other States generally accept the transit of the aircraft through their airspace. Except that ICAO doesn't have many rules about UAVs, well, only one really, that you cannot fly a UAV from one State in the airspace of another without specific authorisation. P.S. It doesn't have anything much about airworthiness of such vehicles either.
- The UK CAA has a booklet about how UAVs are dealt with on their website (can't remember the title off-hand, try a search on UAV). Don't know how much help it will be but you might find it interesting. I'm sure some other NAAs have produced something similar (but don't expect the content to be the same - everyone is on the learning curve when it comes to UAVs.
- Go and find yourself a consultant - a good one - who'll be able to discuss your question in detail. Be prepared to pay for the advice .... someone who knows all the answers about UAVs is going to be expensive!