  Let $\Xi\subset\mathbb R^d$ be a set of centers chosen according to a Poisson
point process in $\mathbb R^d$. Let $\psi$ be an allocation of $\mathbb R^d$ to
$\Xi$ in the sense of the Gale-Shapley marriage problem, with the additional
feature that every center $\xi\in\Xi$ has an appetite given by a nonnegative
random variable $\alpha$. Generalizing some previous results, we study large
deviations for the distance of a typical point $x\in\mathbb R^d$ to its center
$\psi(x)\in\Xi$, subject to some restrictions on the moments of $\alpha$.
