Never leave your log book with a flying school. It is not a legal requirement although some instructors will swear it is.
I don't know whether it is a legal requirement in Australia or not but it certainly is not in other places in the world. I suspect it's more likely a myth that has been perpetuated as a result of restricted business practices that are common in the industry here, aimed at protecting the business of the School rather than anything else. The CASA decreed school training records have more than enough information to verify what training has taken place and to what standard. The logbook is and should be the personal responsibility of the owner.