Thank you cmari and Simon.
Simon, it works either way.
cmari, without a div it hides all of the tiddler, i.e.
=======================================================
! You won't see anything, including this text that is above the conditional part
<<showWhenExists ./nonExistent>><<tiddler ./part2>>
<part part2 hidden>This is the conditional part</part>
=======================================================
And here's my tiddler (requires LoadRemotePlugin and TiddlerTweakerPlugin from TiddlyTools):
=======================================================
{{x{<<showWhen version.extensions.tiddlerTweaker==undefined>>
TiddlerTweakerPlugin is not loaded. Click <<tiddler LoadRemotePlugin with:
[[here]]
[[Load TiddlerTweakerPlugin from
svn.TiddlyWiki.org repository]]
[[
http://svn.tiddlywiki.org/Trunk/contributors/EricShulman/plugins/TiddlerTweakerPlugin.js]]
[[window.story.refreshTiddler('TiddlerTweaker',null,true)]]
[[version.extensions.tiddlerTweaker!=undefined]]
>> to load.}}}{{x{<<else>><<tiddlerTweaker>>}}}
=======================================================
R.