Very roughly, if at all. It depends not only of how much memory those other processes are using, but also on the particulars of the Virtual Memory implementation of the system (if any), the amount of swap space, whether you can overcommit memory etc.
To get back to the original poster's question: the only limit on the size of a variable in Perl is memory. How much that is in practice is difficult to predict, as fglock's post indicates.
CU
Robartes- who will now take of his pedantic hat and quietly shamble off to take a seat in the back of the room again
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