There is no overall SVN repository size limitation in Assembla.

We place no limits on maximum file size or the number of files per commit. 

However, we only allow viewing of up to 200 files in a directory on the web app to control performance.

It would be prudent to keep file and commit sizes in mind when working with SVN as large files and commits can slow down your repo's performance.
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You may also be interested in Assembla's Private Installation on dedicated hardware.