How do you know? If you have 3 or more devices, of standard current requirement(eq, amp, ant), triggered by the same remote turn-on wire. This is not "the law", but it is a good practice. Other than being a good practice, if you know the current drain of the devices that you are attaching to the remote, add up all the values, and compare them to the output current available. If you are at or above the max current available, use a relay.
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Holy crap how does your remote survive? That's a ton of stuff, the rating on the remote wire is MINIMAL. A relay is extremely inexpensive and simple to utilize. Even if your remote can handle it, there really is no reason not to use a remote with anything more than 3 components. Just a precautionary measure that isn't too difficult to take.
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A relay does the same thing as a switch, but has the added value of being able to handle alot more current. They are ablle to do multiple things at the same time, like, choose between inputs/outputs, open connections, or close connections. All of this can be controlled by another switch or as indicated above, by an electronic device.