Homogeneous universal H-fields

We consider derivations \partial on Conway's field \mathbf {No} of surreal numbers such that the ordered differential field (\mathbf {No},\partial ) has constant field \mathbb{R} and is a model of the model companion of the theory of H-fields with small derivation. We show that this determines (\mathbf {No},\partial ) uniquely up to isomorphism and that this structure is absolutely homogeneous universal for models of this theory with constant field \mathbb{R}.