ULN2803A continuous current

afremont:
You can't draw any, it's an open collector output. It only sinks current.

My bad.

afremont:
Each "driver" inside the chip can sink a maximum of 500mA. The datasheet doesn't specify a maximum current thru the ground pin that I could see.

That's my problem.

afremont:
the device will get hot in a hurry if you try to sink 500mA on all 8 drivers simultaneously.

I figured that much. But how do I figure out how much can I sink safely for extended periods (several hours)? I could always hook one up and load it progressively until it releases the magic smoke, but I reckon there's a better way.