I'd like to make multiple copies of a .jpg I've made rain down from the top of the screen, ad-infinitum. Like, imagine small cat's heads raining down from the top of the screen.
I have foggy memories of an effect where I can just replace the default object with my own, but am having no luck finding it.
I swear this is something you can do in AE, I feel like particles are involved, but after a lot of googling around and scratching my head I've just plain run out of gas and so I've come here to ask you all for help. How would I go about making this happen?
You can use custom particles in many particle systems. I don't have time to look up specific tutorials for you but you should find a bunch by just typing custom particle in the After Effects Search Help field right inside AE.
A good introduction to particle tools in AE here:
In short, you can use the CC Particle World effect with a custom texture to do what you're asking.