The HOA is the owners. The owners vote in some board members who do the work on behalf of the majority of owners.
Sometimes the HOA hires some 3rd party management company to handle stuff, but in our case we felt it was wasted money because we would care more about the results. In the end I can see why a lot of owner boards do that as the day-to-day of running the place is obnoxious.
The public spaces were on our property, so our responsibility.
I gotta work this weekend.