Given a degenerating family of Kähler-Einstein metrics it is natural to study from a differential geometric perspective the collection of all metric limits at all possible scales, a typical example being the emergence of Kronheimer’s ALE spaces near the formation of orbifold singularities for Einstein 4-manifolds. In this talk, I will describe, focusing on the discussion of some concrete and elementary examples, how it should be possible to use algebro geometric tools to investigate such problem for algebraic families, leading in the non-collapsing case to an inductive argument identifying the so-called metric bubble tree at a singularity (made of a collection of asymptotically conical Calabi-Yau varieties) with a subset of the non-Archimedean Berkovich analytification of the family. Based on joint work with M. de Borbon.