Unfortunately the YouTube video is apparently unavailable to view in the U.S.
As far as distributing layers randomly in 3D space, you're talking about using Expressions. Specifically the wiggle() expression. Here's how you'd want to set it up.
Create a Null object. Add the effect "Slider Control" to it. On the position property of your layers, alt-click the stopwatch, and put in:
wiggle(0,thisComp.layer("Null 1").effect("Slider Control")("Slider"))
Notice the words in quotes. If your Null object is called something else, and if you renamed your effect, you'll need to change those in the expression accordingly.
Now, if you increase the amount in the slider, that will randomize the position values of your layer within a radius of your slider value. For example, if you set the slider to 100, your layer's position will be put into a random location within 100 (or -100) of it's original position in x, y & z.
This is not really a fantastic way to do it to be honest because the randomness is based on your layers place in the layer order. So lets say you have your layer randomized to the place you like but then you have to move the layer up or down in the timeline. It will jump to a new location in space. So, if you really need to art direct where the layers are in space, I'd say you're better off just placing them by hand.
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