"Franklin now moved to conclude the negotations. On July 10 [1782] he read for Oswald his list of 'necessary' and 'advisable' articles for a peace treaty and implied that acceptance of at least the former was an ultimatum. The 'necessary' articles were full and complete American independence, acceptable American boundaries and fishing rights off Newfoundland and elsewhere; 'advisable' articles were an acknowledgement by Britain of her war guilt, compensation for damages, the transfer to the United States of all of Canada, and freedom from British customs duties for American goods and shipping.
"At the end of July Shelburne finally capitulated to the necessity of accepting American independence. Oswald was given new instructions authorizing the British acknowledgement provided that America became fully independent of France as well; moreover Shelburne wrote to Oswald privately that he was prepared to make a peace on the basis of Franklin's 'necessary' articles. It is important to realize that Franklin won this victory not because America's bargaining position was so strong but because Shelburne was so anxious for peace. *Indeed, he might even have surrendered what is today southern Ontario had Franklin pushed for it.* [Emphasis added.] By showering the Americans with concessions he hoped to cause France, Spain, and the Netherlands to face the necessity of making peace on reasonable terms lest America make a separate peace, thereby freeing tens of thousands of British troops for military operations against the West Indies. Shelburne's generous treatment of America may also have been partly conditioned by the expectation that America would continue to be economically dependent on Great Britain, in which case the granting of generous boundaries to her would do Britian no economic harm." Jonathan R Dull, *A Diplomatic History of the American Revolution* (New Haven: Yale UP 1985), pp. 144-5
http://books.google.com/books?id=W86WS9Z0ycYC&pg=PA144
As for what is meant by "southern Ontario", see Bradford Perkins in *The Cambridge History of American Foreign Relations, Vol. 1 : The Creation of a Republican Empire, 1776-1865,* pp. 38-9:
"[Franklin's 'necessary' terms in 1782 included a demand] that Canada be limited to the territorial limits Britain had, albeit temporarily, established by royal proclamation in 1763. This boundary ran up the Ottawa River through Lake Nipissing to Lake Huron, excluding most of what later became the province of Ontario. The future of Canada would have been extremely problematic, American sovereignty over the entire Canadian west very likely, if the Nipissing line had become the boundary in 1782.
"Nevertheless Shelburne did not hesitate. He immediately told Oswald that, if Frankln would drop the 'advisable' matters, Britain was prepared to settle. The exploratory conversations, Shelburne proposed, should be converted into formal negotiations. Oswald would be commissioned to undertake them. A few days later, the cabinet endorsed this position, although it also decided that Oswald should seek indemnification of Loyalists who had lost property and assurances that prewar debts to British merchants would be paid. A grand chance lay before the Americans, for unless the British reneged they could have had not only a quick peace but one that, by giving them title to the Ontario country, would have doomed Canada's future by confining it to a small enclave along the upper St. Lawrence....
"Unfortunately, the Americans derailed negotiations before the British position was presented to them at Paris. So doing, they almost certainly delayed peace and, in the end, lost the Nipissing country..."
http://books.google.com/books?id=nv3BCrrx3aAC&pg=PA38
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So apparently the Americans lost a chance to get not only Lake Erie in its entirety but all of Lake Ontario and substantially all of Lake Huron as well. As late as August 29, a minute of the Cabinet reads "We will settle the Boundaries of the Province and Contract the Limits of Canada as desir'd by Dr. Franklin."
http://books.google.com/books?id=nv3BCrrx3aAC&pg=PA40 Even the subsequent delay (caused largely by Jay's suspicion of the French) need not have been fatal. See Perkins, p. 44:
"In the last weeks of negotiations, the possibility of even more favorable boundaries almost silently disappeared. All of Canada had never been within their grasp. Although Franklin had asked for it and Oswald seemed sympathetic, neither Shelburne nor any of his colleagues ever considered it. However, Shelburne had repeatedly agreed to accept the Nipissing line. Strachey was authorized to accept that boundary, which was part of Jay's draft, but he was also directed to seek something better, perhaps the 'French boundary', as Shelburne called it. Strachey accomplished this with remarkable ease. Failing to see the importance of the area--the industrial heart of modern Canada--and gratified to receive so much other territory, the Americans retreated to the line of the Great Lakes without even being pressed to do so. It was a fateful act."
http://books.google.com/books?id=nv3BCrrx3aAC&pg=PA44
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So suppose the US gets southern Ontario in the Treaty of Paris? Do you agree with Perkins that "The future of Canada would have been extremely problematic, American sovereignty over the entire Canadian west very likely"?