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Is it possible to ask a specific tab on the tabbar for its position ?

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Is it possible to hide one of the tabs on a tabbar without having the other tabs "slide" up or over into the hidden tab's position?

>>Is it possible to ask a specific tab on the tabbar for its position ?
Not possible , tabs doens't  have strict indexes. In theory, it possible to poll HTML structure and get tab index based on it, if necessary I can provide more detail about such workaround. 

>>Is it possible to hide one of the tabs on a tabbar without having the other tabs "slide" up or over into the hidden tab's position?
Not possible, but you can disable tab, so it will be not-selectable, but still visible, by 
       tabbar.disableTab(id);
In theory, if you will add visibility:hidden to the .dhx_tab_element_disabled css class - disabled tab will become invisible.