How many watts does a cigarette lighter provide?

I'm planning to install a computer in my car. To make it work, I bought a voltage converter that will power both the PC and the TFT monitor.
The question is now, how many watts can the cigarette lighter or the 12V socket in the trunk continuously provide, or would it be better to connect the voltage converter directly to the battery?

I'm particularly concerned about cables melting or even catching fire, which could potentially set the entire car ablaze.

The PC has a maximum power consumption of 150W (according to the power supply).
The TFT, again, 10 watts.
The power converter can provide a continuous output of up to 300W, which is not being reached in this case.

I probably wouldn't do it on a cigarette lighter. I'm not exactly sure how it's protected, but it's probably with a 10A fuse.

Roughly, you would need about 14 amps for a 160-watt load. I would prefer to run a separate wire directly from the battery and fuse it as close to the battery as possible. This way, the supply wire is also protected in case of a short circuit. And don't skimp on the wire gauge.

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'It states that the trunk socket provides 240W of power, while the tilting grill provides 120W.'

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