It is possible to scale out an RDBMS, but it is not easy, and involves some compromises (which NoSQL solutions often tout as part of their basic design as "features"). For instance, you often are forced to give up on cross-server transactions for performance reasons. Search for "sharding" with your chosen relational DB name and you will likely find a lot of solutions with different trade-offs. None are going to be automatic, as you need to carefully manage what data goes onto what server since the data in different tables is related.
For what it's worth, Facebook runs on thousands of sharded MySQL servers... so it is possible. All of the Microsoft web properties also run on sharded SQL Server databases. Usually this involves a good amount of application code changes (which NoSQL solutions also force you to make as well).