on your desk or at your desk? [closed]

Please clarify the usage of right preposition on or at.

For example: That paper is on your desk.

or That paper is at your desk.

The prepositions

• at implies spatial location, or directional.
• on implies vertically atop.

• He is at home.
• She is at work.
• They are at Walmart.
• People are looking at us.

• While we're at it, I might as well remind you to flush the dang toilet every time.
• I am hacking at the problem now.

• She is sitting on the chair.
• We are on the hilltop.
• The cat is on the fridge.

• I am on the problem now. Don't worry.
• He is speaking on the history of the Roman empire.
• The television channel comes on air at 5 am.

Therefore, see the difference ...

• She is sitting at my desk.
• She is sitting on my desk.
• The boy is speaking at his mother's desk.
• The boy is yelling at his mother's dog.
• The boy is yelling on his mother's desk.
• The boy is speaking on his trip to New Zealand last week.

The paper is {on/at} your desk

• Idiomatic use of desk = a virtual work space, especially in news reporting or editorial endeavours.

  • The news desk of Larry King. The latest edition of today's events is at Larry's desk.
  • Please make sure any submission for drafts of your novels are at the editor's desk before 2016/01/31.
  • The paper on the advantages of CMOS analogue design should be at the conference submission desk by noon Aug 1, 2016.

• Physical desk

  • He found the paper at his desk. I have no idea if he found it on, under or beside his desk. But it is on his desk now.

Today, Harry will be speaking on his desk being burned to ashes last week. He intends to sit on his desk when he speaks on his no longer existent old desk. He will be telling us on his old desk, like as though he is telling on us to our boss. He will be telling on his old desk about all the secrets it held.

Since he will be targeting at his old desk, he might as well be telling on the hatred he thinks his desk had on him. Since he will be at his old desk, he might as well be on his old desk, on their mutual love-hate relationship with each other, while sitting on his new desk and delighted at his new desk.

In fact, he was at his new desk this morning writing his speech on a piece of paper. That paper is now on his desk. He plans to submit it to CNN's news desk hoping they would publish it. But we know it won't be on CNN, because such a silly paper will never be found at CNN's news desk.

The correct usage is:

That paper is on your desk.

The preposition at is used in a slightly different situation:

You should be at your desk during office hours.

In American English we would almost always say

The paper is on your desk.

and on is used when we refer to something being in contact with the surface of an object. This often means on top of a surface, such as a desk. This can also refer to a vertical surface, as in The fly is on the wall.

At is used to specify a location as a point in space. It just means where your desk is. It does not mean on top of your desk, like on your desk would usually mean. We might say the guest is at your desk. Or maybe the umbrella is at your desk. Technically, we could say the paper is at your desk but it is not idiomatic.

On is most likely right in this case but not necessarily. If it's on the bookshelf next to your desk, and you're in another room, at your desk is just enough information for your colleague to know how long it will take to fetch it. If it's in the desk drawer, at, in and under are all more appropriate than on. It would be unusual to use anything other than on for an item to which it was definitely applicable, or could be assumed to be applicable, such as a keyboard. If you said on when it wasn't literally true, the only person who would be bothered is someone you'd sent to look for it.

I'm used to southern British English, some relevant influences here may be engineering terminology, and large open plan offices ("at my desk" would be equivalent to "in my office" or even "in my cubicle")