When it's everyone's responsibility, it's no one's. When it's everyone's project, it doesn't get done.
Somebody needs to run it.
The diffusion of responsibility is too large when people are busy and focused on other tasks. But when it becomes their own personal responsibility to carry out that project or that task, it takes a new level of importance.
What makes a good project owner?
Passion for the project. They need to be excited about it or at the very least, believe that it really matters.
Vision for the outcome, but humility to listen. People are looking for vision from the owner. Something to latch on to. Then they have an opinion to agree or disagree with. And that's where the magic of collaboration begins.
Connections to carry it out. If something needs to get done that requires delegation or a specialized skill, the owner needs to know who or know how to find the who quickly. And they need the ability to generate buy-in from others. (This is tied to the passion for the project. If they have it, they can communicate it to others. If they don't, buy-in will be hard to generate.)
Autonomy. The freedom and responsibility to make decisions moves projects forward. If the project owner is not given the freedom to make decisions, give the project ownership to the true decision maker or bring them up to speed to the point where they have the ability to make those decisions (provide more information, build trust, etc.)
Can you pass the ownership to someone else?
Absolutely. There can be a number of reasons to pass off ownership: different skills required, more resources available elsewhere, incompetence, lack of belief or passion in the project.