Here's a guy who is good at duplication:
But on the serious side, you can only do it with vector shape layers in any sort of automated way.
But with expressions you could set up a composition to calculate the necessary angle rotations as you duplicate the layer:
With only the layer that you want to duplicate in the comp, put this expression on the rotation value:
Duplicate it once then put this expression on each anchorPoint value except the top one which you will change to adjust the radius of the circle:
Then duplicate as many times as you would like and adjust the anchorPoint of the top layer.
Using this method you'll have to create different compositions for each ring of pictures you want to make since the expression is dependent on then number of layers in the comp.
Depending on how much control you need, you might want to play with CC Kaleida as a simple alternative. Multiple kaleidoscopic layers can produce amazingly complex patterns.
As Andrew said, CC Kaleida and other tiling tools (including AE's own Mirror and Motion Tile) will give you plenty to work with. And then there's also things like Card dance, Trapcode form or Trapcode Echospace that can repeat particles or 3D layers and create patterns in a multitude of ways....