If my app deletes a post it made to a user's wall, will all likes and shares made by other people also be deleted?

Lets say I have a FB app I've created, and for whatever reason the server code for the app is responsible for posting stories to the app user's wall (using a token).

Now let's say we want to take down that post at a later date - easy, right? Because the app created the post, it owns it, and using the ID it received originally it can take that post down. (I presume the ID I get back is actually an "object id" referring to my content, rather than specifically to the post on the user's wall - correct?)

Here's the thing though. What if one or more friends of the user shared that story to their own wall - what if this happened a number of times, spreading through the friend relationship tree further and further. Does my app still have the power to remove all of these posts, because it created the original post?

Additionally, what if the original user deleted the post themselves from their wall, but not until it had been shared by his/her friends? Would this have the same effect (delete everywhere), or would it only be that one specific post being removed? Would my app get an error when it tried to delete the post itself if the post had already been deleted by the user?

The reason I ask is because, if my app deleted the original post that it made to the user's wall, I would want all of the shared posts or likes to also be deleted, no matter where they were down the friend chain. I don't want to delete my original post and assume all is well, only to discover that because it was shared several times down the chain that it is still visible somewhere.

In case it's relevant, the "post" my app will make would require a custom image and a specific return URL - I tried the /user_id/links graph API and it didnt work (there's a bug with it). So I'd be most likely using /user_id/feed to make the post.

if my app deleted the original post that it made to the user's wall, would all of the shared posts also be deleted from everywhere?

Yes

What if the original user deleted the post themselves from their wall, but not until it had been shared by his/her friends? Would this have the same effect?

Yes

How did I know this? I tested it.

I posted a status update to a test user Betty

Then had three other test users share it one after the other

So Tom shared it > Joe shared what Tom shared > Patricia shared what Joe shared

Then for completeness I had Betty share it again

On delete, all posts are gone from all test users, including the re-share Betty made.

As long as the user shares via the action link all subsequent shares will be deleted if the original is deleted.

But if the user manually copies it or saves a photo then re-uploads then no.

In terms of documentation, you have to bite bullet and realize there is no comprehensive documentation for Facebook and not all Facebook engineers know all features about Facebook. There are many items that haven't been able to get a word from Facebook about, and that's when I test things. That's what developers do. Create new test paths, do coverages, make branches and arrive at a conclusion