  We study the bilipschitz equivalence type of tree-graded spaces, showing that
asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of
groups containing a cut-point) only depend on the bilipschitz equivalence types
of the pieces in the standard (resp. minimal) tree-graded structure. In
particular, the asymptotic cones of many relatively hyperbolic groups do not
depend on the scaling factor. We also describe the asymptotic cones as above
"explicitly". Part of these results were obtained independently and
simultaneously by D. Osin and M. Sapir.
