How does Tomcat redirect verbose:gc console output to catalina.out?

It has nothing to do with code; the catalina. Out file is not a "real log", it's just a file into which the standard tomcat startup command pushes all it's output.

Tomcat must indeed be using System.setErr() and System.setOut(). There's a great discussion about how that works elsewhere on this site: java: "final" System. Out, System.in and System.

Err?

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