Most discussions I've about recovering adamantite have reached the conclusion that it's best if PC's can't just "recycle" the metal from items they've recovered. This can be achieved by having it so that adamantite can only be forged once, thus an adamantite item is only useful in so far as that particular item is useful. Alternatively, adamantite could be "reforged", but the process to do so would be more expensive than the value of the metal itself, making it an unattractive proposition.
Personally, I like the first option. It's easy to imagine that part of the forging process is what imbues adamantite with its extraordinary hardness. Thus, re-forging the metal simply isn't possible.
I allow PCs to recycle adamantite/adamantium, but it's a process. In my games, mithril is to adamantite as iron is to steel. Adamantium is the alloy of mithril and "powerful magical enegies [PME]." In order to recycle adamantium, they must first melt it (requiring the fire from a great wyrm). That strips off the PME, which is lost. This leaves 75% of the original adamantite as mithril. It can then either be reforged as mithril or turned into adamantium (if the PCs have access to the PME).
When it is a suit of armor or the like, PCs usually take it as is. If not, it is still fairly portable. The Tree in Shackled City is another matter. This monstrosity would be exceedingly hard to break apart into transportable pieces. And good luck getting the dragon to come to you to melt it down then and there.