The object of our research is the Poisson–Laguerre tessellation, i. e. a random Laguerre tessellation whose generator is a Poisson marked point process with intensity t. We are interested in the asymptotic behaviour (as t → ∞) of functionals of the tessellation – e. g. the perimeter of the cells, the ratio of volumes of the neighbouring cells - in the case where the weights of the random generator are not uniformly bounded. As it turns out, to obtain a normal approximation for the functionals of the Poisson– Laguerre tessellation, it is useful to study the behaviour of the distance to the furthest neighbour of a typical point of the point process. In this talk we will present some properties of this characteristic, which were derived using the concept of tempered configurations.