In reply to ericoides:
MB de Courmayeur is completely in Italy.
From a legal point of view, the definition of the frontier passing on the main summit of MB in the 1861 Turin treaty between Italy and France is still valid, as that section of the border wasn't changed after the peace treaty between the two nations in 1949 (after WWII).
The definition of 1861 was inequivocal. However, when the first official French map of the new border was made, the cartographer (a French officier called Mieulet), produced a map with the line of the frontier passing on MB de Courmayeur. It's not clear how this happened - definition of the actual, physical frontier line was, back then, a methodical process based on a sort of "contradictory" between the land survey officiers of the two nation, who would have revised every meter of the border to decide where to place the division line. It's unlikely such a process happened for MB, partially because of the physical difficulty to get there, part because there's no surviving written transcription of "definition process" of the frontier here (as it should have happened). In other words, only the 1861 treaty says that the main frontier should pass for the highest summit of MB.
It's not clear why Mieulet decided to change the frontier location. It was thought for years it has been "suggested" by the French government (to put the summit entirely into French territory), but the latest theory is that he did it all on his own.
A further complication happened in 1946, when the Haute Savoye authorities decided to put an end to a century old diatribe between the communities of Chamonix and those jolly fellows in St. Gervais Les Bains, as the latter had produced some land register evidence "demonstrating" that the area of the summit dome of Mt. Blanc going from the main summit to MB de Courmayeur on the W (Miage) side was owned by St. Gervais itself. This could (by the way) allow legally St. Gervais to change its name in "St. Gervais - Mt. Blanc", and - if you don't know - it's the basis of the current St. Gervais mayor claim he has the right to limit access to Mt. Blanc and establish a permit system. It must be noted that from the point of view of international law, land register evidence can't be used to establish the border between nations.
The shifted frontier thing was repeated on every French map afterwards, and for many reasons the Italian government(s) that followed never make an actual step to have the situation corrected, until 1988, when (after on a request from Italy), a join commission was established to re-establish the correct frontier. Then Italian ambassador in France Napolitano produced large evidence to support Italy's position on the controversy, but after almost 8 years of discussions, the commission was dissolved (under French request). The whole thing was discussed again (this time in Parliament) and further pressures were made to establish another commission to close this issue once for all, but recently France made the point that after Schengen treaty, all controversies related to borders internal to the EU must be solved at EU level.
The whole thing is far less academical than it may appear at first, as a re-definition of the frontier from a cartographical point of view would have two very practical consequences:
1) Define St. Gervais claims on the summit of MB (with all that implies, given the current Mayor plans on it!)
2) Define (a lesser know problem) who owns Col du Geant, and all the infrastructures there
