It should depend on the context mode for the service. You can control this via an attribute:
[EnableClientAccess()]
[ServiceBehavior(ConcurrencyMode = ConcurrencyMode.Multiple)]
public partial class SomeService : LinqToEntitiesDomainService<SomeEntities>
{
I believe the default option is ConcurrencyMode.Single
.
From MSDN: "Setting ConcurrencyMode to Single instructs the system to restrict instances of the service to one thread of execution at a time, which frees you from dealing with threading issues"
So, to answer your question, the global list
is not shared between calls to your service (unless you make is static).