What did I do
 

I'm finished wiring my 582 16 hp refreshed briggs ,the pto ,battery ,lights ,magneto etc . It fires right up like a champ no smoke and purrs. I went to shut it off with the key in the off position and removed the key and it will stay running. I have to trip the mower safety switch to get it to turn off. All of the ground wires are connected terminals all cleaned free of rust no rust even on the nuts ,bolts or washers. I used the original harness which worked great with the original engine and this problem was not there. I have the ground between the firewall and frame like it should be ,volt meter and hour meter grounded together on the rear of the dash the battery grounded to the box with the frame the solenoid grounded to the box also what am I missing? The magneto has one wire that is grounded to the top of the motor.

Doubt check your kill wire at the magneto...

I might be a grammar Nazi, but you might get more response with some punctuation. I'm not saying I have the answer, but I quit reading about half way through because it was a chore to understand.........

Me too...... :ThumbsUp:

Copy edited due to compulsive career disorder.

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I've finished wiring my 582's 16hp refreshed Briggs, including the pto, battery, lights, magneto, etc. It fires right up, runs like a champ with no smoke. I went to shut it off with the key and it keeps running. I have to trip the mower safety switch to get it to turn off. All of the ground wires are connected, terminals all cleaned, no rust even on the nuts, bolts or washers. I used the original harness which worked great with the original engine and this problem was not there.

I have the ground between the firewall and frame like it should be, volt meter and hour meter are grounded together on the rear of the dash, the battery is grounded as well as the solenoid. The magneto has one wire that is grounded to the top of the motor. What am I missing?

Clarify what you are talking about.
:Huh:

He is saying that with the original engine and original wiring harness,--- no problem.
Now, new engine with original wiring harness,--- has problem.

CTS 582, On your Magnetron coils (those are the the things with the spark plug wires coming out of them), there is (are) small lugs with spade wire connectors. The way the Briggs (and Kohlers) get shut off is that when you turn your key to the off position a ground gets put on those lead(s). The safety switches do the same thing. I would look for a dirty/loose connection at your key switch.

Is the key switch old? In all the tractors I've bought, the key switches have needed replacement about 80% of the time.

I had this problem one time and it was the key switch.

you inadvertently polarized the starter/gen to positive ground by shorting one of the reg wires to ground and it's back feeding the ignition. Disconnect your battery,recheck your regulator wiring. Reconnect the battery and start.