You can find market share information in Business Insights: Global. Search for the industry or interest, and select the "rankings" tab from the profile. Once you have selected "rankings", you can then click on "market share". This will provide you with a list of relevant market share information from Market Share Reporter.
Mintel Market Research Reports provides a range of market information, frequently through the category level, including market size and forecasting, complete with market drivers that illustrate the forces that shape a category or market. Search by company, brand, or product type. Select "Market" then "Brand/Company."