self supporting staircase?

[Robbox]

I don't know anything about staircases and how they are supported. But I have some photos of ours and some questions I need answering...
I think the photos are fairly self-explanatory. We want to remove the two walls that you see in the second photo.
What investigations could be made to find out if the walls are actually doing any supporting?
I do know that the joists run parallel to the wall on the left in the third photo.
I've also visited a friends house, who has the exact same staircase style that also intrudes into the kitchen like ours, but that part is simply boxed in with no support.
So I imagine it has to be possible.
Thoughts and comments welcome.

 

[Doggit]

Actually, the photos aren't that self explanatory, but having looked at them several times, I suspect the non door wall in the cupboard under the stairs, is supporting the landing as you step down the stairs, so you would need to make sure that the joist that runs paralel to the cupboard wall, is doubled (and possibly witha flitch beam), and that'd then support the joists that go on to that non door wall.

 

[Robbox]

Actually, the photos aren't that self explanatory, but having looked at them several times, I suspect the non door wall in the cupboard under the stairs, is supporting the landing as you step down the stairs, so you would need to make sure that the joist that runs paralel to the cupboard wall, is doubled (and possibly witha flitch beam), and that'd then support the joists that go on to that non door wall.

There's me thinking a picture tells a 1000 words... NOT!
Here are four more photos that I hope show a better picture!
I've taken a measurement from outside wall to the non-door wall in the kitchen...870mm.
Up on the stairs, that same 870mm from the same outside wall comes to a point back from the end of the staircase itself.
What, if anything, would this indicate? To my untrained eye it looks like the wall sits underneath the second from top tread/riser.

 

[Doggit]

What, if anything, would this indicate? To my untrained eye it looks like the wall sits underneath the second from top tread/riser

Exactly, so it may well be supporting the joists that go from the top of the stairs, to the wall on the far side of the stairs. Now it may be that the joist that runs over the wall with the door in it, is sufficient to support a header that then supports the joists leading to the top of the stairs, and that's what you need to determine before you take the walls out.

 

[chappers]

Does the newel in the 3rd picture go to the ground and is the string over the bottom string. That could be what's holding the whole lot up including the landing.
A shot up the stair from the bottom would be more useful