I think it heavily depends on the company and the project. See explanation at the end.
In our company, DBAs are reponsible for:
- installation and upgrades of the DB engine
- creation of schemas (db users)
- adjusting default privileges
- adjusting DB engine parameters like cache size
- monitoring and maintaining tablespace and physical storage
- monitoring hardware usage
- scheduled maintenance operations, for example gather schema stats
But they are NOT responsible at all for:
- performance of particular queries
- creation and maintenance of database structures and procedures
- adjusting grants
I know some companies where even these latter tasks belong to DBAs as well.
I think if there are several SQL developers working on a DWH or a big OLTP system, DBAs will only do the maintenance tasks to provide a reliable framework.
On the other hand, if there is no big SQL development going on, mainly just native or web coding and there are no SQL experts, the DBA will take all points including performance tuning and every little datamodel modification.