In the desktop verion of the TreeView there is a way to have 3 checkbox states by setting tree.override.nodestyle = CheckBoxTriState
Is there any way to accomplish this with a WebTree ??
I believe this is doable with custom code, but it will require custom javascript code in the client-side NodeChecked event - you can check all child nodes, uncheck parents if needed, etc.
Darrel has a nice example of using checkboxes on the client-side - more information can be found in this forum thread - and this can be a good place to start:
http://forums.infragistics.com/forums/t/2861.aspx