Black Hole Growth When a black hole increases in size by engulfing matter, does this matter fall into the event horizon or does it just rotate around the accretion disk? 
EDIT: Clarified the beginning of the question.
 A: Matter in the accretion disk is not (yet) inside the black hole. It is orbiting, and it can even escape. In fact, some of it must escape for accretion to happen at all: The disk has too much angular momentum to be accreted, and so some material must be ejected, carrying off excess angular momentum, in order for the rest to fall into the hole.
The general idea is that matter in the accretion disk slowly makes its way inward (dependent entirely on how well angular momentum can be transported outward with help from magnetic fields). Once it reaches the innermost stable circular orbit or thereabouts, it plunges toward the black hole rather quickly. This defines the inner edge of the disk, and is somewhat above the event horizon.
Now whether or not the matter ever does fall in is another question, but it's as much a question of semantics as physics.
A: It doesn't just rotate around the accretion disk. As to what actually happens to it isn't clear-cut. Most people will say the infalling matter goes right through the event horizon all the way to the central point-singularity in finite proper time. But check out The Formation and Growth of Black Holes on mathspages: 
"Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural 'limit' of this process is that the clock asymptotically approaches 'full stop' (i.e., running at a rate of zero). It continues to exist for the rest of time, but it's 'frozen'..."
Most people just aren't aware that there's this other GR interpretation. And some people who are, such as the author of the article, tend to discount it saying things like this: 
"Therefore, if the 'frozen star' interpretation gave equivalent predictions for all externally observable phenomena, and was logically consistent, it might be the preferred view. However, we saw above that the idea of a frozen star as an empty region around which matter 'bunches up' outside an event horizon isn't viable".
There's an error here, which you can appreciate by thinking about a hailstone. You're a water molecule, and you alight upon the hailstone's surface. You can't pass through this surface. However other water molecules can settle around you and bury you, so the surface passes through you. So you can effectively pass through the surface. In similar vein the black and its event horizon can grow. I should add that on top of all this there are "firewall" issues, but that's one for another day.  
