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If most of these concurrent accesses are read (e.g. SELECT), SQLite can handle them very well. But if you start writing at the same time, blocking competition can be a problem. Much will then depend on how fast your file system is, since the SQLite engine itself is extremely fast and has many smart optimizations to minimize competition. Especially SQLite 3.
For most desktop and laptop / tablet / phone applications, SQLite is fast enough as there is not enough concurrency. (Firefox makes extensive use of SQLite for bookmarks, history, etc.)
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