Dividing independence for ultraimaginaries is neither symmetric nor transitive. Moreover, any notion of independence satisfying certain axioms (weaker than those for independence in a simple theory) and defined for all ultraimaginary sorts, is necessarily trivial.
Itay Ben-Yaacov. "Discouraging results for ultraimaginary independence theory." J. Symbolic Logic 68 (3) 846 - 850, September 2003. https://doi.org/10.2178/jsl/1058448443