SPOILERS FOR SEASON 4
So, for those of you who haven't seen it, there's apparently this deleted scene in the end of Season 4 where Ten gives TenII a chunk of the TARDIS and tells him to "grow your own."[link]
I am kindof glad that this wasn't included in the final version of the show, but at the same time, I'm REALLY glad it exists for the fans - the idea of TenII growing a TARDIS is too adorable.
I also like to imagine him attempting to get the chameleon circuit stuck as a police box, landing it on streets in the UK in the 60s and trying to get it to stick. Who knows if Pete's universe even has them. Maybe the closest he'll get is one of those red telephone booths....