>The Forest Clearing consists of multiple clearings in the woods, while the Deepest Clearing is another area, capable of holding up to 10 Pokémon, reached by traveling through the northern parts of the Forest Clearing. Most Pokémon are automatically transferred to the first clearing once materialized from the Dream World; however, some Pokémon such as Arceus are specifically designed to appear in other clearings. To transfer them to the Deepest Clearing, the player must speak to the Pokémon and refuse to catch it; the option will then appear. Alternatively, if the player's party and all of their Boxes are full, then this option will appear by default. Players begin with 6 sections to their Forest Clearing and one Deepest Clearing; however, if they are all full with 20 Pokémon each, players' forests will grow larger to accommodate more Pokémon.
Unlimited, as the forest expands as more Pokemon are added.
Source
