Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams, Geometry & Topology, 9 (2005), 2319--2358.

Abstract Let G be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin-Razborov diagrams for G. We also prove that every system of equations over G is equivalent to a finite subsystem, and a number of structural results about G-limit groups.