  The parameter space of the simplest extension of the standard model, is
studied in the light of the 125 GeV Higgs boson discovery. The Hill model
extends the scalar sector of the standard model with a real singlet, that mixes
with the SM Higgs boson. The two-loop SM renormalization group equations are
completed with the one-loop Hill equations. Stability up to the Planck scale is
possible without tension with the other parameters. An extension with more
singlet fields, in particular a higher dimensional (HEIDI) field is presented.
