The solids go into the grow beds. Put in some red worms and they will help break it down so the plants can absorb it. If you have the cycle time correct, the beds will not dry out.

I posted a thread on how to size your biological filter.
Calculating your Bio-filter
It is actually tiny compared to the fish volume to convert the ammonia and nitrites. The bigger issue is nitrate buildup. This is a function of how fast your plants take up nutrients. This means you need surface area and not volume. If you harvest all your plants at once, it doesn't matter how large your grow bed is. A good rule of thumb is that the bed volume should be 3 times the fish volume, and the surface area of the grow bed needs to be large enough to support the plants needed to keep the balance. The bed volume includes the growing media.