Passing Criteria for Product Backlog

Does all Product Owner define all passing criteria ahead of time when they define the product backlog?

Would doing so be a necessary condition of refinement, if work is to be deemed ready as per the Scrum Guide?

it is up to the PO to break up the backlog to different team since it is self organizing. 

If the PO did that, how would team self-organization then be free to occur?

 Does all Product Owner define all passing criteria ahead of time when they define the product backlog?

I think it is a good idea to capture any known criteria at the time of creating the Product Backlog Item.  But based on refinement activities, there may be more identified or some removed.  The final passing criteria is usually not known until the Product Backlog Item is ready to be pulled into a Sprint.  

Also when you have multiple Scrum Team, how does a Product Owner help reduce the dependency on product backlog? Scrum Master help setup the process but the it is up to the PO to break up the backlog to different team since it is self organizing. 

There is no reducing the dependency on the Product Backlog.  Scrum Teams are completely dependent on the Product Backlog to know what work needs to be done on the Product. 

In my opinion when you have multiple teams working from the same Product Backlog the best way to help Developers self-organize is by creating a clear Product Goal and helping each team form a focused Sprint Goal.  The Sprint Goal will help teams to select items from the Product Backlog. Since each Scrum Team has independent Sprints, crafting Sprint Goals that are complementary but separate will allow all of the Scrum Teams to operate independent of each other but make concerted movement towards the Product Goal.  This is not a job for the Scrum Master or the Product Owner alone.  This will involve all of each Scrum Team so the Product Owner for multiple teams will have to participate with each team.  Same for the Scrum Master if they are also shared among teams.

The final passing criteria is usually not known until the Product Backlog Item is ready to be pulled into a Sprint. 

But the item can also be more refined during the sprint, so more criteria could appear during the sprint, no?

But the item can also be more refined during the sprint, so more criteria could appear during the sprint, no?

Yes you are correct but that should be less of an occurrence.  In my experience when the acceptance criteria changes while work is in progress, it is usually done to fit the work that has been done.  This is a very tenable situation because that can often lead to delivering an item that does not meet the original intent.  Sprints are typically 2 weeks and that is a short duration to make these kind of adjustments.  If a team finds themselves needing to change acceptance criteria often I would suspect that their refinement might not be adequate.  But even if the team is doing a 30 day Sprint, I'd be leery of acceptance criteria changing frequently. 

@Daniel Wilhite: thanks man ! A clear cut answer. I have seen in few threads, instead of giving them a clear cut answer. They ask requester multiple questions (some of them sounds riddle to me). At times i dont see point of asking those questions to the requestor. He / She doesnt have much idea on the content. Thats reason they have started a thread in this forum. We all people should respect it.

Product Backlog has the list of items that need to be worked upon. Only the most clear items are listed at the top of the Product Backlog and Developers select from top items after discussion with Product Owner. The passing criteria of these items is listed in Sprint Goal and Definition of Done. In Sprint Planning passing criteria (or Sprint Goal) is decided based on what is known. As and when more is known, Sprint Backlog gets updated in the Sprint. The Sprint Goal is not changed in the sprint. After Sprint Retrospective more stringent criteria gets added to Definition of Done. For a new Sprint there is new Sprint Goal, based on what is known. 

When you have multiple Scrum Teams or single Scrum Team, Product Owner is responsible for creating Product Backlog. After a thorough discussion with Product Owner, Developers from multiple Scrum Teams, select the items from Product Backlog as per their level of expertise. While selecting, the Scrum Team or Product Owner clarifies them of any dependencies, and the selection gets refined. Product Owner doesn't assign Product Backlog Items to different teams. Its Developers, who select items.  Developers then break up the work from Product Backlog items into one day work.