I noticed that the size of the logcat buffer varies on different devices. Assuming I have root permissions on my device, is there a way to change the buffer size of the main
No, as per here it seems that the log buffers on the device are 64 KB. The timestamp, process ID, and log level are stored in a compact format, so you may actually get more than 64 KB of formatted data out of logcat -d -v
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See also Stack Overflow question What is the size limit for Logcat?.
Anyway, for saving logs elsewhere, you have Reading and Writing Logs. That maybe could help you.