Only the commissioner can set the rest of the league to auto-pick. Individual teams do not have that option, so the draft timer will always run out and then make a selection.

For those who don't want to wait the full time, the commissioner can press on the current tile and select "Force CPU Auto Pick".
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The auto pick option will select players based on the owner's queue, which is available to you during and leading up to your league's draft.

Using the above photo as an example, the CPU would auto pick DeAndre Hopkins for me if he was available at my next pick.

If there aren't any players remaining in my queue, it will take into consideration what positions my team needs, and it will take one of the higher-ranked players available.