There is actually a thorough treatment of it in. Lin et al. 2017. Selecting path models in SEM: A
comparison of model selection criteria. Structural Equation Modeling 24:
There it is listed as ABIC. This is an excellent review and simulation study, best I have seen yet. Very complicated topic with an "it depends" answer to which one(s) are 'best'. Frustratingly, AICc is left out (a standard in biology), but CAIC is included.
Thanks to you both for the help. I guessed it was the sample-size adjusted one, but needed to be certain.