Nested view: All messages are displayed (as in flat view, All), but rather than being ordered by posting date/time, they are ordered by thread (as in threaded view). Further, individual messages are indented in the same manner that the message list is indented in threaded view, which provides visual context for the reader.
It is far more efficient to have an entire message thread (or a large subsection, in the case of a paged view) available to read at a given time since, for the most part, individual messages tend to be short, and take less time to read than it takes to load a new threaded view. Threaded view is in general just an annoyance because of the need to constantly reload the thread view. It is only useful for long threads with few new replies.
Because individual conversations within a single thread can diverge, a flat view is problematic in terms of trying to maintain the conversational context. This leads to problems of over-quoting, and increased redundant bandwidth usage. It also means that a failure to over-quote leaves you searching for past message references when you want to put a reply in context. Finally, it means that, in avoidance of both of those issues, people will tend to either reply to the first post in a sub-thread rather than read through and find whether the topic has already been responded to, or ignore the earlier parts of the sub-thread because it's too difficult to group and read the information together.
Example: The forum software that AnimeOnDVD.com used before moving to UBB was DCScripts. Here's a thread from their support forum that shows how nested view looks:
DC Scripts forum thread Note: there's a View in Linear Mode / View in Threaded Mode link near the top of the page that may need to be toggled. It also may not be the best example, since most of the threads there tend to be pretty linear (as might be expected in a support forum), but it should at least show what it looks like.
Pink Jazz says that lack of page number and lots of scrolling are drawbacks for this mode. Personally, I'd rather have lots of scrolling than lots of clicking, and the lack of page numbers is something I actually prefer. I find threaded and flat views to be clumsy and awkward to use in any but the simplest of conversational threads.
In general, lack of a nested view has been the single biggest gripe people on AOD.com have had since the changeover (from what I've seen, anyway). A home-brewed hack that put it back in the previous version of UBB busted with the latest upgrade. I and many others would greatly appreciate it if it were added to the core code.
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David