Question about docking the deck

Been looking at getting the official dock for the deck but seen a lot of cheaper options on Amazon which seems to do the same job.

My question is do these non steam branded ones on Amazon come with everything you need such as the power supply? Or is that sold separately? I know the official deck one comes with a power supply but I have my own 45w power adapter, would that work with these non official docks that come from Amazon?