Why is a storm's rain usually north of the center?

Just looking at a radar loop of Dennis (see here) and noticing that, as usual, most of the precipitation is to the north of the center. Most big storms seem to be like this, hurricane or not. What’s the reason, and is this reversed in the Southern Hemisphere?

WAG: most of the rain is north of the eye because most of the land is north of the eye. It looks to me as if the storm is pulling water off of the Gulf and dumping it over the South.

If I read this link correctly, hurricanes draw water from the ocean as air is drawn towards the eye. Of course, the air follows a spiral path due to the storms rotation. Once the air reaches the eye, it turns upward where it meets with air descending from the upper atmosphere and then begins an outward path. Most of the rainfall takes place relatively close to the eye (i.e., within two hundred miles or so.) The storm’s rotation means that the water taken off the ocean to the south is at the north side of the storm when it is released.

Along with water, the storm lives off of heat from the ocean. I don’t think that the earth is able to provide as much heat, so my guess is that the water vapor condenses over land as the air cools. At least it seems to me that tropical storms don’t really dump their water until they’re well inland.

If it appears that most of the rain falls north of a hurricane’s center, it is due to the fact that most hurricanes move in a northerly direction. If you looked at hurricanes that moved in an easterly direction, you would find that the most of the rain falls east of the storms center. Most of the rain falls to the side toward the direction of movement.

Another WAG here, but I always thought it had to do with the warm humid air colliding with the drier cooler air (that’s usually found north or east of a storm) that helps create all the rain. Same reason thunderstorms tend to follow a SW to NE direction.