  We discuss the relation between pluripolar hulls and fine analytic structure.
Our main result is the following. For each non polar subset $S$ of the complex
plane $\mathbb C$ we prove that there exists a pluripolar set $E \subset (S
\times \mathbb C)$ with the property that the pluripolar hull of $E$ relative
to $\mathbb C^2$ contains no fine analytic structure and its projection onto
the first coordinate plane equals $\mathbb C$.
