  We consider (not necessarily proper) colorings of the vertices of a graph
where every color is thoroughly distributed, that is, appears in every open
neighborhood. Equivalently, every color is a total dominating set. We define
$\td(G)$ as the maximum number of colors in such a coloring and $\FTD(G)$ as
the fractional version thereof. In particular, we show that every claw-free
graph with minimum degree at least~$2$ has~$\FTD(G)\ge 3/2$ and this is best
possible. For planar graphs, we show that every triangular disc has $\FTD(G)
\ge 3/2$ and this is best possible, and that every planar graph has $\td(G) \le
4$ and this is best possible, while we conjecture that every planar
triangulation has $\td(G)\ge 2$. Further, although there are arbitrarily large
examples of connected, cubic graphs with $\td(G)=1$, we show that for a
connected cubic graph $\FTD(G) \ge 2-o(1)$, and conjecture that it is always at
least~$2$. We also consider the related concepts in hypergraphs.
