A computational device receives a request to copy a source logical block of a thin provisioned source logical unit to a target logical block of a thin provisioned target logical unit, wherein in thin provisioned logical units physical storage space is allocated in response to a write operation being performed but not during creation of the thin provisioned logical units. The computational device generates metadata that stores a correspondence between the source logical block and the target logical block, while avoiding allocating any physical storage space for the target logical block in the thin provisioned target logical unit.