I'm doing some research about cooperative documents between nations regarding ATC; does anybody can mention interesting cases of agreements across the globe? Relations such as Swiss/Others and Hong Kong/China (during British domain) comes to my mind. Also, is there known, famous cases of events (incidents/accidents) caused by disagreement between ATC of different countries you could mention?
You could look into the situation regarding the airspace above northern Cyprus. This relates to 'disagreements', rather than 'agreements'!
Cyprus was invaded by Turkey in 1974, and since then the country has been split into two sections with a UN 'buffer-zone' between the two. The northern portion of Cyprus is not recognised as a separate country (well, not recognised by many States ...), and whenever 'Cyprus' is mentioned they are talking about the Greek half on the southern side of the island. Turkey still insists that the northern half is a separate country.
There are a few air-corridors that pass north-south (and v-v) over the country. A flight going from the north to south will be handled by Turkish ATC until they are at the FIR boundary mid way across the sea between Turkey and Northern Cyprus, whereupon they are told to contact 'Ercan Control'. Ercan is an illegal ATC station in the occupied part of the island which is not recognized by the International Civil Aviation Organization (ICAO). ICAO only recognises the legal government of Cyprus and has issued instructions to aircraft operators to obey only Nicosia ACC when in the Cyprus FIR.
In practise, flights generally ignore that instruction, and contact Nicosia ATC directly.
Heading in the opposite direction flights are told (by Nicosia ATC) to contact Turkish ATC, completely ignoring Ercan Control.
In practise, there are extremely few flights flying these routes, so the problem rarely arises. The use of Ercan Control is limited to Turkish flights heading from Turkey to northern Cyprus.
See Cyprus ATC