Answer
The maximum size single file that ArcGIS, ArcInfo Workstation and ArcView 3.x can typically address is 2.147 GB. This is a normal limit for 32-bit software applications. The absolute number is 2**31 - 1 bytes (2147483647).
Note:
This is a signed value, thus half of 2**32.
This limit is in effect until ESRI software is re-coded fully for 64-bit operating systems and microprocessor architectures.