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
dimH(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
α-H\"olderian functions is also discussed