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The standard behavior for IDE - when the server was started from IDE, when you remove it, or close IDE, IDE automatically stops the server. But if you remove server using Server Manager dialog, it will not be stopped. This is an inconsistency.
The issue is still reproducible
Fixed. Behaviour is the same for server manager now. Checking in src/org/netbeans/modules/j2ee/deployment/impl/ui/ServersCustomizer.java; /cvs/j2eeserver/src/org/netbeans/modules/j2ee/deployment/impl/ui/ServersCustomizer.java,v <-- ServersCustomizer.java new revision: 1.16; previous revision: 1.15 done