J.W.
You are putting the cart before the horse. It isn't that you can't J. get someone declared incompetent but usually people gain durable power of attorney and medical power of attorney first. Then incompetence becomes part of exercising those powers.
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If you already have those documents then wait! Seriously. Call the attorney who drew them up and have him explain but those are powerful documents that will allow you to gain control in an emergency.
You speak as if you are concerned with the time you need to step in and those documents are all you need to be prepared for the time you need to step in.
So at this point call the attorney because elder care laws are not federal (reads universal) so state laws apply. I could tell you what happens here but likely it isn't the same in your state.
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Oh, also make sure you don't jump the gun, if he isn't incompetent that will be proven and I would imagine it will piss him off enough that he revokes that power, which he can legally do at any time until he is declared incompetent.