JavaFX Tab fit full size of header

I want the tabs in my tabpane to fit the complete size of the tabpane which they are in. So basically there shall be no header area visible, everything should be covered by the tabs.

I have 2 problems here:

• How can I make the tabs dynamically fit the width of the tabpane?
• How can I fit them to the correct height, and remove the little spaces between the tabs? I suppose this is done via css, but I don't quite know how.

greets