By default, the default size of a database on exchange 2003 is 16GB.

With Exchange 2003 service pack 2 installed the default limit is 18GB but can be extended up to 75GB per database for the standard version of Exchange 2003.
This can be done by adding a registry key.  See: https://cloudbuild.co.uk/?p=473

The enterprise version of Exchange 2003 allows upto 8TB per database