I was looking for a description of the DropDown modes provided by the Search Box Scope dropdown. Finally found them in a whitepaper, and thought I would post them here as well to propogate that knowledge.
The DropDownModeEx property supports the following values:
• HideScopeDD: Do not show the search scopes drop-down list.
• ShowDD: Show the drop-down menu, and include the search scopes defined both for the SSP and the site collection.
• ShowDD_DefaultURL: This option has the same behavior as the ShowDD option, but provides the default selection on what is provided in a query string.
• ShowDD_DefaultContextual: This option has the same behavior as the ShowDD option, but provides the default selection on the first scope in the list that is identified as the most relevant contextual scope.
• ShowDD_NoContextual: Shows the search drop-down list with only the SSP-defined scopes.
• ShowDD_NoContextual_DefaultURL: This option has the same behavior as the ShowDD_NoContextual option, but provides the default selection for the query string.