How is anybody to be certain they know the full answer for all international destinations?
The answer is, if you want full detail, by consulting the legislation of every country to be overflown or visited. As a shortcut, you could try the Chicago Convention which details the documents to be carried on international flights:
Article 29
Documents carried in aircraft
Every aircraft of a contracting State, engaged in international navigation, shall carry the following documents in conformity with the conditions prescribed in this Convention:
(a) Its certificate of registration;
(b) Its certificate of airworthiness;
(c) The appropriate licenses for each member of the crew;
(d) Its journey log book;
(e) If it is equipped with radio apparatus, the aircraft radio station license;
(f) If it carries passengers, a list of their names and places of embarkation and destination;
(g) If it carries cargo, a manifest and detailed declarations of the cargo.
There are further requirements in Annex 6 Part II
2.4.2.2 Aeroplanes on all flights shall be equipped with:
...
d) the following manuals, charts and information:
1) the flight manual or other documents or information concerning any operating limitations prescribed for the aeroplane by the certificating authority of the State of Registry, required for the application of Chapter 2.3;
2) current and suitable charts for the route of the proposed flight and all routes along which it is reasonable to expect that the flight may be diverted;
3) procedures, as prescribed in Annex 2, for pilots-in-command of intercepted aircraft;
4) visual signals for use by intercepting and intercepted aircraft, as contained in Annex 2; and
5) the journey log book for the aeroplane
Having said that, within Europe the provisions of
Regulation (EC) No 785/2004 of the European Parliament and of the Council of 21 April 2004 on insurance requirements for air carriers and aircraft operators also applies, meaning that you also need proof of insurance.
In fact, the convenience of a single set of rules for your international flight in Europe will only be achieved when the rules are standardised across its states. For rules where the UK currently has more liberal regulation than the European norm, that seems to be a painful process for UK pilots.