  We describe limits of line bundles on nodal curves in terms of toric
arrangements associated to Voronoi tilings of Euclidean spaces. These tilings
encode information on the relationship between the possibly infinitely many
limits, and ultimately give rise to a new definition of limit linear series.
This article and its first and third part companion parts are the first in a
series aimed to explore this new approach.
  In the first part, we set up the combinatorial framework and showed how
graphs weighted with integer lengths associated to the edges provide tilings of
Euclidean spaces by polytopes associated to the graph itself and to its
subgraphs.
  In this part, we describe the arrangements of toric varieties associated to
these tilings. Roughly speaking, the normal fan to each polytope in the tiling
corresponds to a toric variety, and these toric varieties are glued together in
an arrangement according to how the polytopes meet. We provide a thorough
description of these toric arrangements from different perspectives: by using
normal fans, as unions of torus orbits, by describing the (infinitely many)
polynomial equations defining them in products of doubly infinite chains of
projective lines, and as degenerations of algebraic tori.
  These results will be of use in the third part to achieve our goal of
describing all stable limits of a family of line bundles along a degenerating
family of curves.
