Subject: Why does comet dust spread out along the comets orbital path?

Comets are theorized to be ``dirty snowballs'', that is, lumps of rock and dust all held together by frozen gases. As they near the Sun, the gas can melt (or sublimate; go right to vapor) which loosens the other junk. Bits and pieces of the comet can then drift away from the parent comet.

There are forces on these flotsam. The solar wind is one, and light pressure from the Sun is another. These are fairly gentle forces, and can push the castoff material away from the comet. They do indeed take on new orbits, but the bigger material doesn't change all that much. Over centuries, the orbits can drift quite a bit, but there is usually still a clear tie to the parent comet, because there are characteristics of the orbits that are similar, like ellipticity, time of perihelion (closest to the Sun) passage and the like.

There are many websites about comets and meteors. Try Gary Kronk's Comets & Meteor Showers site, or The International Meteor Organization for more info.