In The Return of the King, when the Fellowship finally parts ways, Pippin says that he wishes they each had palantiri so they could communicate with each other over long distances. Aragorn responds:
Only one now remains that you could use, for you would not wish to see what the Stone of Minas Tirith would show you. But the Stone of Orthanc the King will keep, to see what is passing in his realm, and what his servants are doing.
-The Lord of the Rings, The Return of the King, Book VI, Chapter 6: "Many Partings"
I assumed that the King in question was Eomer, the King of Rohan. But in a comment on another question, someone suggested that Aragorn was talking about himself in the third person (i.e., "But the Stone of Orthanc I will keep, to see what is passing in my realm, and what my servants are doing"). This seems strange to me, and we never really hear Aragorn speak this way elsewhere in the story.
It also isn't clear why Aragorn would want two palantiri - one should be enough.
Is there any evidence to clarify this issue? Did the Stone of Orthanc go to Eomer or Aragorn?