Chewtobacca said: I swear Darth Maul's body wasn't seen falling down in two halves though, when I saw the film, but maybe that is my faulty memory.
Your memory is perfectly intact. A small quantity of reels of Phantom Menace where Maul isn't cut in half went out in some areas of the USA (which is where I assume you are). It was an early cut of the film, made incase Maul's bisection garnered a higher rating (which in the end it didn't).