Ok, I see, you have a parented object that you want to create a motion path for so as to copy it to illustrator.
After some trial and error, I discovered a way to do so:
1) Make sure that the anchor point of the object you want to create the path for is in the center (or at the point you want the path to follow)
2) Create a null with the following expression for its position:
M =thisComp.layer("Layer to Follow here");
pos = M.toWorld(M.anchorPoint);
pos
(Now your null should follow the object.)
3) Use Animation > Keyframe Assistant > Convert Expressions to Keyframes for the Null’s position
4) Delete expression from the Null
5) Copy position keyframes
6) Create a new solid with a mask
7) Paste position keyframes to mask
(You should now have a mask path of same shape)
8) Copy mask path
9) Paste in Illustrator (note: the path may be rather large initially, so you may have to zoom out to see it)
If all goes well, you’ll now have a path in Illustrator that follows the object’s motion exactly.
You’ll have points at every keyframe, but the good news is that they are bezier paths. Interestingly enough, you can control the amount of points created by changing the frame rate. AE does a great job creating bezier curves between the keyframes.
This is a great idea, glad you asked. It opens up an interesting way of generating Illustrator art from motion.