The ship in the picture is the John F. Kennedy-class Space Carrier Vehicle Nuclear. It's not actuly as flat as it looks - there's a wedge-shaped hull underneath, but it's too dark to see

Please note that this model was stolen from the Lancer Reactor, and several maps were tea-leaved from HLPers - Aldo's landing pad, for example. Eventually, I'll get around to asking formal permission to use the stolen stuff.
Lastly, there were other big warships in S:AAB, but they were only seen in the final two-parter. Basically, the production team built models as they need them. The first epsiode was a little odd because the Earth fleet consisted of only carriers. Eventually, we saw battleships and cruisers - I do have meshes for these, but I've to evaluate their suitability for POFfing.