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There are infinite sequences of graphs { G} where | G| = n such that the minimal dominating sets for G × H fall into predictable patterns, in light of which γ ( G × H) may be nearly linear in n; the coefficient of linearity may be regarded as the average density of the dominating set in the H-fibers of the product. The specific cases where the sequence { G} consists of cycles or path is explored in detail, and the domination density of the Grötzsch graph is calculated. For several other sequences { G}, the limit of this density can be seen to exist; in other cases the ratio $${\frac{\gamma (G_n \times H)}{\gamma (G_n)}}$$ proves to be of greater interest, and also exists for several families of graphs. [ABSTRACT FROM AUTHOR]