Importing Illustrator artwork outside the artboard to after effects without cropping

Theres a simple solution to this. And its a fix EVEN if you have already started animating layers in After Effects. Sometimes altering things in illustrator after animating can be dangerous, but this is NOT one of those times.
Simply open the illustrator file in illustrator, go to Objects > Artboards > Fit to Artwork bounds.

This will increast the size of the artboard to beyond all your graphics layers and when you save and go back to AE, the layers will NOT be cut off.

Mark

I stumbled across an odd characteristic that you may be able to use to your advantage. While After Effects is not fully compatible with Illustrator artboards, it does seem to consistently import only from the bottom (last ordered) artboard. Therefore, if you have an Illustrator layout that you use for other things, like exporting to JPEG or linking in other documents, you can simply add a separate, overlapping, bottom artboard which encompasses all of the artwork and still use the other artboard(s) for those purposes.

What I mean by "After Effects is not fully compatible with Illustrator artboards" is that when you have more than one artboard, you cannot select which one to import the graphics from. The Illustrator feature of multiple artboards was added a long time ago. You'd think other Adobe applications would have all caught-up by now. What I mean by "odd characteristic" is that most Adobe applications not fully compatible with Illustrator artboards will only import Illustrator artwork from the top (first ordered) artboard instead of the bottom.

Just double click on the area and then you can drag the artboard from the corners to uncover your artwork. If you're having problems selecting it, just lock the other ones 

create another artboard that is big enough to contain all your artwork. keep the original artboard and don't change the order of the artboards since Ae will pick up the 1st artboard as the composition dimensions which is what you want. save the file. now in Ae you can move the artwork and won't see it cropped.

FYI the HD preset in illustrator comes with 2 artboards by default, that resolves any of these issues. 

What is not on the AI artboard, won't be there in AE - it is that simple. So you either scale your artwork until it completely fits on the artboard, or your enlarge your artboard until it covers all the artwork.

There is no need to work with large comps in AE if your artwork is full vector. Just scale the artwork down in AI to 1920px. You can freely scale it in AE if you need it. Just don't forget to activate continuous rasterization on all layers and comps involved.

If you have rasterized parts in your artwork, you have to work with large comps. No workaround here if you don't want quality loss.

*Martin