  Using a local monomialization result of Knaf and Kuhlmann, we prove that the
valuation ring of an Abhyankar valuation of a function field over a perfect
ground field of prime characteristic is Frobenius split. We show that a
Frobenius splitting of a sufficiently well-behaved center lifts to a Frobenius
splitting of the valuation ring. We also investigate properties of valuations
centered on arbitrary Noetherian domains of prime characteristic. In contrast
to [arXiv:1507.06009], this paper emphasizes the role of centers in controlling
Frobenius properties of valuations rings in prime characteristic.
