Web vs Desktop

Since the first webpage, not enough time has passed. The tasks and possibilities of the Web changed from day to day. You may notice that some web applications are so heavy - they do not at all fit into the ideology of the multi-browser, that I just want to put them on the Desktop. Those. thereby taking a step back, the opposite of what we did with the web.

So where is the shaky border: beyond which - the application can no longer live in the narrow framework of the desktop, or it is more convenient to take and move it back, say, a small icon near the clock.

The trends of such sparadic jumps are already visible. For example, the Mozilla Foundation with Prism and Weave . Or even closer integration with Adobe with its fresh Air .
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And what services would you prefer to use on the Desktop and vice versa?