Clearing symbol values, removing symbols from memory and general garbage collection.

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Global context seems to be shared between kernels when using Clear?

I am trying to understand the following behaviour, and determine if it's a bug in Mathematica 10. I am using Mathematica 10.3, and can't reproduce this behaviour under Mathematica 9. The test outlined ...
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What are the differences between Clear, Remove, ClearAll, Unset and TagUnset, when to use which?

What are the influences of these operations on things like UpValues, DownValues, OwnValues and whether the kernel knows the symbol? When do I use which? I know ...