The string size is limited by the amount of memory available on the server. Whether this string can be successfully saved in the session will depend on the session storage engine used.
If you use a ready-made file-based session repository, then most likely you can write a file that is larger than the available memory. If, however, you used, say, memcache, then you could be more limited.
However, in practical terms, if you keep so much in a session, you ask this question, you are probably abusing sessions!
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