It's just absorbed by the ground - never to be seen (or smelled) again. I'm presuming it adds nutrients to the ground but when I dig a new pit a year later there's nothing there but sand and a few disintegrating bones.
If I'm planting something I use stuff from the pile that's been through the chipper - no kitchen wastes in that pile.
Things planted or trnasplanted within the last year or so: kaffir lime tree, angelica, basil, rue, lemon verbina, epazota, turmeric (yellow and white), Jerusalem artichoke (accidentally), horseradish, sage, marjoram, oregano and papyrus reeds.
The papyrus is doing very nicely, about 7 feet tall and spreading fast - it burst it's original planter. I thought it would need more water than it does, but it's quite tolerant.