This is a Doctor Who 10.5 piece. Now on Pete's World with Rose, he finds a gift left to him my the original Doctor.
Apparently, in the original script the Doctor was meant to give a TARDIS coral to the half-Human Doctor under the assumption that a whole new TARDIS could be grown from it, but it was later cut. - reference from Doctor Who wikiReference pose
courtesy of *SenshiStock
EDIT: Updated the link to the deleted scene on youtube.
Obviously this includes spoilers if you still have yet to see the end of season four.