While this is probably easy for announcement lists or ezines, predictions can be a little more difficult for discussion lists, especially if they are unmoderated.
Most service providers regulate the number of posts per day, week or month.
The other important thing to remember is the service provider's size. If you're a business trying to move 100,000 emails a day, you could very well crash a small provider's servers, or at the very least your messages would be delayed several hours. Service providers who mover large bulk lists probably cost a little more, and you probably won't find a free service to this for you. In the end you will be glad you picked a service that could handle large volumes of mail even if it does make a bigger dent in your wallet. You should also note that most service providers pricing favors larger lists.