Adrian:
One must not forget about the Scotch tape! Got to have Scotch tape (the type you can write on) - especially for larger scale analysis efforts.
When I am in the discovery phase on a larger scale analysis project, I follow the flow of data from as high of a level of abstraction as possible. Since I am in discovery, typically, I do not know how the data is going to ultimately flow: left, right, up, down, in, out, - all over the place - changing direction at a moments notice, a ton of cross overs. Plus I constantly need to squeeze in things that I forgot. The first couple of iternations look like a big mess, but, are just clear enough that I can read them. When I run out of room while diagramming, which happens frequently, I quickly scotch tape another piece of paper on and keep going. The thing is to keep going. Trying to create a Visio of a big mess, while still in a heavy requirements discovery phase, is a real initiative killer.
Now when it comes to walkthroughs of sub-systems, then Visio (or whatever) can really help. And, after the first couple of iterations, when things are realively firmed up, I create a set of parent-child Visio diagrams of the whole systems. Word processing after modeling is fine.
FYI: Visio and the like also hinder a larger scale analysis effort by making me frequently switch mental gears from thinking about flow from a high level of abstraction to thinking about detail-oriented software commands. The mental-gear switching can be very exhausting!
Tony