What, exactly, is transferred along supply lines?

The current accepted answer seems a bit unclear to me, and may actually be inaccurate. I'll try to explain better, by my understanding, here.

The only remote resources that are available to the player, in settlements that are linked via supply lines, are those which can be used for crafting. Even then, those resources can't simply be collected from the Workshop's inventory. The only way to access them is by using them in the crafting process.

This means that you can't drink Purified Water that's stored at a remote location, but you can use it to create Vegetable Starch. You won't be able to take a Blood Pack out of a connected workshop and put it in your inventory to heal yourself, but you can make a Stimpack with it. Etc.

This also means that not all Aid items will be available across a supply line. Meat that's already been cooked, drinks that have been made, or drugs that have been blended will most likely not be accessible because most of these items aren't used up by any recipes.

Mods are available to be added to a weapon if they are in a remote settlement's workshop.

Weapons and Armor will not automatically be broken down into components when crafting, so will not transfer via supply line.

Furniture, Walls, Turrets, Shops and other craftable settlement stuff will not transfer via supply line, with the exception of crops. When one stores a Mutfruit tree or a Tato plant, it simply shows up in the workshop as a Mutfruit or a Tato, and those items transfer for the purposes of crafting.

If junk in a remote, connected workshop is automatically broken down, the leftover components are deposited into the local workshop (the one the player is crafting from). (This needs further verification from somebody else - only 95% sure on this).

Nukapedia claims that food and water will be shared across the line, for consumption by settlers, even though the UI might not reflect this. More testing is still required on this, but from what I can tell, food and water is indeed transferred along supply line, but not in an obvious way. My observations:

• Excess Food/Water production is not shared in a way that is obvious from the UI - you can't tell that Settlement B with 10 food shortage is taking food from Settlement A which has 10 food surplus.
• However, a settlement with insufficient production will not report a Food/Water shortage (exclamation mark in the UI) as long as there is food and water in its workshop.
• Excess Food/Water production ends up deposited as actual items (Mutfruit, Tato, Purified Water) in the workshop of the settlement that has the surplus (many players take the excess to sell for caps).
• The surplus Food and Water items in the settlement's workshop will disappear on their own, and show up in the settlements with insufficient production, and thus those settlements will not report shortages in the UI.
• However, if one consistently empties all the surplus Food and Water items from the settlement with excess production, the connected settlements with insufficient production will eventually run out of Food/Water items (Mutfruit, Purified Water), and when empty, will start reporting shortage crises in the UI.

So it appears as if Food and Water is transferred via supply line, but not instantaneously like crafting components. Further testing is required to determine the details of how it is transferred; also if this is a total misreading of observation or not.

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TL;DR:

• Mods, Aid, and Junk will transfer as needed for crafting.
• Nothing will transfer for the purposes of picking up into inventory.
• Weapons/Armor do not break down into components automatically, so will not transfer.
• Craftable settlement items (furniture, turrets, walls) that are then stored in the workshop will not transfer, with the exception of crops.

*Testing Needed

Please comment/edit if you can help answer any of these, to further clarify how supply lines actually work.

• Food/Water: Are surplus Food and Water items (Mutfruit, Purified Water) in settlements transferred instantaneously at a particular time (vendor refresh? 10:00am every morning?)? Or are they actually transferred by the provisioner assigned to the supply line (do the Food and Water items in a settlement disappear when the provisioner hit the settlement with the surplus, and reappear when the provisioner reaches the settlement with insufficient production?). If the latter, is the AI smart enough to transfer enough items along long supply line chains? e.g. if the settlements are connected A->B->C, and A has a surplus water production of 20 and both B and C are short by 10, will the A->B provisioner take 20, so that the B->C guy can take 10 and leave enough for both B and C?
• Food/Water: If all your settlements have a cumulative production of 250 water and you only have 150 settlers, for a surplus of 100, and you sleep for a month, you don't end up with 3000 Purified Waters. Similarly, my workshops don't have 10000 Mutfruits piling up. What's the limit on excess Food/Water, and when does it correct? What's the ideal frequency and time to grab the surplus and sell so that extras aren't lost to this correction, and how much should one leave behind?
• Scrap: What happens if an item on the remote end of a supply line has components other than, or in excess of, what is needed for the item being crafted? Does the extra stuff come to the local settlement, get left at the remote settlement, or disappear?

Only item classes which can be accessed from workshops will be transferred between settlements. Unfortunately, this does indeed mean that weapon, armour, and ammo are not transferred, and neither are food and water resources.