Total value of a company is not related to influence. The largest are conglomerates, thus subject to impact on each segment. Which stock market they are allied with depends on several factors, including whether they get favorable treatment or not.
Who holds the stock is an important factor; e. g. BP is roughly 50% UK held, 50% US held.

BHP-Billiton (BR) is the largest mining conglomerate, but it's diversified. largest income from oil-gas; many companies are larger in this field, thus have as large or greater impact in that field.
BHP leads in coal, and has much iron interest; quite large there.

Vale, a U.S mining comglomerate, is almost as large.
Rio Tinto (BR) is also a giant
Shenhua (China), no. 4, is very influencial in the market, because of its control of rare earths.
(Canada has two companies in the top ten, UK has 4, the U.S 3, China 1, India one).
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Corporations with largest market value:
Apple
ExxonMobil-2
Petrochina
Microsoft
IBM
Industrial Bank of China
Royal Dutch Shell-1
China Mobile
China NP-5
Sinopec-6
General Electric
Chevron-8
Petrobras
Walmart-3
BHp Billeton
China Construction Bank
HSBC
BP-4
Conoco-Phillips -9
Toyota -10(nunbers are for total revenues)

A fairly diversified list.