(This is my first time trying to post an embedded notebook here in Community. I hope it went well, and I hope the technique demonstrated in the notebook proves useful.)

I call them "fake" in that the results do look like Voronoi diagrams, but there's not much else you can do with them. To use my first example, VoronoiMesh[] is certainly easier to do stuff with than the fake I made with DensityPlot[].

In an e-mail, Christopher Wolfram suggested that one might be able to use WatershedComponents[] on the resulting pictures, but I have yet to do those experiments.

Regarding the example with multiple objects that you mention, I did something like that in this mathematica.SE answer.

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