Jason Brimhall shows all you can do by default with the public role in SQL Server:
It is amazing what some people will do that just doesn’t make sense. Granting permissions to the public role is one of these cases. That behavior also explains why there are documents and procedures for hardening the public role (here and here).
If necessary, I recommend locking down your public role. It will make your job a little easier and give you better rest at night.
Read the whole thing.