Map in the Infobox
The map in the infobox is not canoncial. The map incorrectly does not show Anórien to be a part of the Reunited Kingdom of Arnor and Gondor. Anórien was still a part of Gondor during the War of the Ring and was never a part of Rohan. Although The Lord of the Rings does never mention the borders of the reunited kingdom it is unlikely that it did not include Anórien, which was still a part of Gondor during the War of the Ring.
The information about the borders of the Reunited Kingdom during the reign of Elessar is speculative. In the Lord of the Rings the borders of the reunited kingdom of Arnor and Gondor during the reign of Elessar are not mentioned (especially not in Appendix A II The Kings of the Mark Third Line). The exact status of the Shire, of Fangorn Forest and the Treegarth of Isengard and of Drúadan Forest are not known from the wording of the grants. It is only mentioned that the Shire was made a "Free Land under the protection of the Northern Scepre" in Appendix B Later Events concerning the Members of the Fellowship of the Ring S.R. 1427, but not whether this means autonomy and self-rule as part of Arnor or it not being a part of Arnor. However it is mentioned that the Hobbits say "Our King, we call him" about Elessar in Appendix A I (iii) The North-kingdom and the Dúnedain. It appears odd to calle somebody "our" King if one's Country is not part of the Kingdom. It is also mentioned that King Elessar made the Thain of the Shire, the Master (of Buckland) and the Mayor (of the Shire) "Counsellors of the North-kingdom" that Appendix B Later Events concerning the Members of the Fellowship of the Ring S.R. 1434. It would seem odd to make leaders of a realm councillors of a kingdom if the leaders of that realm are not part of the Kingdom.