JavaFX TreeView: remove expand / collapse button (disclosure node) & functionality

I want to have a TreeView that has all of its children permanently expanded, and I don't want the user to be able to expand or collapse any of the children.

To do this I've found that I need to do the following:

• Remove icon with CSS (Done)
  • Change expand and collapse image TreeView JavaFX 2.2
  • [edit] Above link should be used to change image; to remove completely, use this solution: https://stackoverflow.com/a/27831191/4430591
• Remove double click functionality (Done)
  • Disable TreeItem's default expand/collapse on double click JavaFX 2.2
• [edit] Remove ability to collapse / expand using keyboard arrrow keys (Done)
  • Given in José Pereda's solution below ( https://stackoverflow.com/a/27831085/4430591 )
• [edit] Remove ability to right click for a ContextMenu (Done)
  • Given in José Pereda's solution below ( https://stackoverflow.com/a/27831085/4430591 )
• Remove icon's clickablity (How do I do this?)
  • [edit] solution: https://stackoverflow.com/a/27831191/4430591

Even though the icon is no longer visible, it's still clickable. I don't see any way of filtering this; I only see ways to be able to respond to it after the fact.

Also, if I'm missing anything else that I need to do to ensure this functionality, please let me know.

I feel quite silly. I think this was mostly just a matter of not knowing what that darn arrow was called. Apparently it's a disclosureNode? Maybe that's common knowledge.

In the custom defined TreeCell, all I did was add this line in the updateItem method:

setDisclosureNode(null);