Pluripolar hulls and fine analytic structure

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 ℂ we prove that there exists a pluripolar set E ⊂ (S × ℂ) with the property that the pluripolar hull of E relative to ℂ2 contains no fine analytic structure and its projection onto the first coordinate plane equals ℂ.