I have looked in the Forum's thread information about this problem; in the following thread:
Maximum mailbox size
Sam writes that the aforesaid limit of 2 GBs depends on the dimension of the file .zdb on the PC client.

But I don't want to download the whole contained of account e-mail in a file .zdb, because otherwise I would have connected in POP3.
Have I understood badly? Is there another way to configure outlook to avoid this? Or Outlook Connector creates really a file .zdb of the same dimensions of the e-mail account?
I hope to have understood badly, otherwise it would be impossible for me to use this type of tool.
Fabio