  Given a completely metrizable space $X$, let $\mathfrak{par}(X)$ denote the
smallest possible size of a partition of $X$ into Polish spaces, and
$\mathfrak{cov}(X)$ the smallest possible size of a covering of $X$ with Polish
spaces. Observe that $\mathfrak{cov}(X) \leq \mathfrak{par}(X)$ for every $X$,
because every partition of $X$ is also a covering. We prove it is consistent
relative to a huge cardinal that the strict inequality $\mathfrak{cov}(X) <
\mathfrak{par}(X)$ can hold for some completely metrizable space $X$. We also
prove that using large cardinals is necessary for obtaining this strict
inequality, because if $\mathfrak{cov}(X) < \mathfrak{par}(X)$ for any
completely metrizable $X$, then $0^\dagger$ exists.
