For an exemple, when they have distributed "Porco Rosso" in France (I don't remember the year), this Ghibli anime has won (in term of amount of tickets) against the Disney animated of the moment (I don't remember which one). Since this time, every Ghibli movie have been distributed only between two Disney movies...
Actually, in France, even if there's Narnia in theatres (but it's really too different of an anime, so, no conflict), we have the pleasure to have "Pompoko" in theatres. I haven't seen it yet, but I will soon! Anybody saw it?