  Let $K$ be a compact set in $\rd$ with positive Hausdorff dimension. Using a
Fractional Brownian Motion, we prove that in a prevalent set of continuous
functions on $K$, the Hausdorff dimension of the graph is equal to
$\dim_{\mathcal H}(K)+1$. This is the largest possible value. This result
generalizes a previous work due to J.M. Fraser and J.T. Hyde which was exposed
in the conference {\it Fractal and Related Fields~2}. The case of
$\alpha$-H\"olderian functions is also discussed.
