Yes, it will vary depending on what you wish to do.
If your assignment is set up to be used with Turnitin plagiarism checking (normally .doc /.docx /.pdf essay file submissions), the maximum allowed file size is 40mb.
If a document is over 40mb in size then it might be possible to make the document smaller by compressing the images used in the document. Microsoft have a guide on how to do this found here: Reduce image file sizes
When using eAssignments without Turnitin checking (normally submitting SPPS or Excel files), then we recommend that files are no larger than 250mb. This is because it can be difficult for some internet connections to upload a file, despite the internet connection showing a good download speed.
If you want to use eAssignments for video submission, we generally recommend using Panopto instead: https://elearn.southampton.ac.uk/panopto/students/