This is CH Purrmunn Amelia of Caleb-Cats, She was our very first Persian. She was a black smoke.  Ami was 5yrs old in the photo above.

A black smoke Persian has a white or near white undercoat that is around 50% or less of the hair color but from roots to mid way, then the tips from mid way to the very tips are colored in her case her tips were black.   Imagine a flame the  smoke is at the tips.

We on occasion get solid blacks with a smokey outer coat this is still a black just faulty color and not a black smoke.  A black smoke is similar to a shaded silver but has more tip coloring.

The smoke gene is dominant there for one parent must have the undercoat to produce it.  It does not skip generations.  Smokes, Shadeds, Chinchillas, Silver tabbies that have a undercoat, a himalayan thats points are of any of those colors bred to a solid or a white masking any of these can produce Smokes.

We no longer work with smokes. More info about smokes can be found at these links.

http://www.cfa.org/breeds/profiles/articles/persian-smoke.html

http://www.cfa.org/breeds/standards/persian.html#Shaded/Smoke

Below are a few examples of non smoke cats with faulty color. One is a solid black as he matured the smoke color went away. The other is a solid chocolate, most of her smokey color went away with age as well. But no white roots on either of these cats, and the faces are very solid in color, a smoke has white roots even under the facial hair at the roots.