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Given a user keyword query, current Web search engines return a list of individual Web pages ranked by their "goodness" with respect to the query. Thus, the basic unit for search and retrieval is an individual page, even though information on a topic is often spread across multiple pages. This degrades the quality of search results, especially for long or uncorrelated (multitopic) queries (in which individual keywords rarely occur together in the same document), where a single page is unlikely to satisfy the user's information need. We propose a technique that, given a keyword query, on the fly generates new pages, called composed pages, which contain all query keywords. The composed pages are generated by extracting and stitching together relevant pieces from hyperlinked Web pages and retaining links to the original Web pages. To rank the composed pages, we consider both the hyperlink structure of the original pages and the associations between the keywords within each page. Furthermore, we present and experimentally evaluate heuristic algorithms to efficiently generate the top composed pages. The quality of our method is compared to current approaches by using user surveys. Finally, we also show how our techniques can be used to perform query-specific summarization of Web pages.