It shall look and behave like the firebug button on the toolbar of Firefox:
1) if clicking on the left part, onClick is fired
2) if clicking on the right part, a menu is dropped down

In additions, it shall also support the look and behavior of the bookmark button of Firefox: it supports only dropdown. It could be done by

Alternative 1: detect if onClick is listenered. If not, it is the bookmark button (always dropdown).
Alternative 2: two different component (combobutton and dropdownbutton)
Alternative 3: two different mold