I have tried with CSS to remove the border from SplitPane but it can't be done. The best I could do was change it's color and/or make it thicker.
The problem is that some UIs use nested split panes and each level adds a border. This makes some areas appear with very thick looking borders where there should be one pixel of border. The result is quite ugly. It should be possible to remove the border on SplitPanes via CSS (-fx-border-width: 0;) so they can look good even when nested.