Dugundji's Canonical Covers, asymptotic and covering dimension

Given a nowheredense closed subset $X$ of a metrizable compact space $\tx$, we characterize the dimension of $X$ in terms of the multiplicity of the canonicals covers of the complementary of $X$, specially in some particular cases, like when $\tx$ is the Hilbert cube or the finite dimensional cube and $X$, a Z-set of $\tx$. In this process, we solve some questions in the literature.