Version 0.990 will not need so much video memory thanks to texture compression. At Full HD (1080p) screen resolution, you need no more that 6 GB graphics card.
At LOD 0, fully loaded view from the surface consumes just 600-700 Mb of VRAM (look at the LandNode reading on the left). Detail textures are enabled, texture compression is enabled. This is just terrain system consumption, and this scene is loaded at startup, so 600 Mb is only room taken by terrain nodes visible on the screen (4003 nodes were generated, LandNode-Allocated reading). Engine reserves some extra nodes to let you rotate camera and fly around, typically 3x times more than this (12900 nodes, LandNode-Max). So I may say that terrain engine requires 2 GB of video memory at LOD 0.
But this is only terrain engine. Add another 1 GB of static textures and buffers, some room for stars/galaxies/ships. Total 3 GB for stable work at LOD 0. SE works even with lower amount of VRAM, it dymanically reallocates it as needed (for example, removing long ago used terrain nodes to free memory for ship textures then you spawn a ship). But if you have just 1.6 GB of video memory, you can load such scene with no problem. But if you start moving, nodes which out of view will be deleted almost immediately and replaced with new nodes. So then you decide to retucn back to initial point, you will see loading process again. So 3 GB is better.
At LOD 1.5, memory requirements rises up. Now this scene generated 1.5 Gb of terrain textures, 7314 nodes were created, 20000 nodes reserved. Fully used reserve is 4.2 GB of VRAM. Add 1 GB of static resources, so you need 5.5 GB graphics card for smooth playing.
At LOD 2, engine generates 2.2 GB of textures, 10000 nodes, but reserved limit is still 20000 (so again, 6 GB graphics card will be enough). Reserved limit can be raised in the config, but I don't see purpose for this. Nobody playing at LOD 2, it can be used just for taking extreme screenshots from a stationary point. Because loading time is huge, about 5 minutes. Note that framerate is much lower than at LOD 1.5 and LOD 1 - because graphics card needs to render 10000 meshes with a set of unique textures each.
You can sel LOD 3 and even more through the console command, but I don't believe any GPU can handle that. Also, with the new terrain engine, extreme LODs improves nothing. You may notice some improvement of texture and mesh detail between LOD 0 and 1, but LOD 2 is almost the same as LOD 1. Yes, terrain is splitted on more nodes, but their texture detail is excessive, so they get downscaled by GPU resterization anyway. LOD 1 is already pixel-to-pixel resolution.
So I may say that if you playing at Full HD resolution, you need 6 GB at most extreme. If you have 4k display, then LOD 0 will take nearly the same VRAM as LOD 1 on 2k, because of doubled resolution, so 6 GB will work again. You need more VRAM only to play at excessive LOD 2 in 4k resolution. To take screenshots at LOD 2 in 4k, 6 GB will be enough I think.