From my previous post, I've managed to create an image of how I see the 'Yggdrasil' in my head. Here I will describe it.
The tree itself is large and almost dwarfs the rest of the ship. Wrapped around the tree is walkways leading to habitats on the tree and suspended around it. The base has more mechanical features including the walkways that house the Hawking Drives. The base leads to the underside that houses the Engineering and cargo spheres around the base. There tendrils that looks like roots emerge from the bottom. The special 'Erg' containers are connected to a ring that rotates around the ship creating it's propulsion. Also on the underside is the Hawking Drives. A forcefield surrounds the top half leaving the mechanical parts in the void.
I will be mocking up an image of the treeship in Maya and Photoshop to further get my image across.