For any admissible normal function $\nu$ over any dimensional base, we construct by the method of log geometry a Néron model such that $\nu$ extends to a section of the model over the boundary. The model is Hausdorff and is a relative log manifold.
"Néron models for admissible normal functions." Proc. Japan Acad. Ser. A Math. Sci. 90 (1) 6 - 10, January 2014. https://doi.org/10.3792/pjaa.90.6