For now, do this using a custom internal renderer (non-shared). When we implement the next-gen L&F, we may want to make the tab buttons themselves containers, and the content and close buttons subcomponents within the container.
I think "close a tab" is a very common operation. I implemented this myself in some ugly way but I hope pivot can support this ASAP.
Alfred, did you implement it in Pivot? If so, you could submit it as a patch in this ticket.