Going in alphabetical order, I think it is fitting to start with one of the most iconic carry heroes in Dota 2: Anti-Mage, aka. Anti-Fun. Well, this time he's bound to be fun - I predicted him to be in the trash tier of supporting potential.
Let's look at what we have to work with. Anti-Mage is very mobile, with quite a bit above average movement speed and a blink ability. Supports love mobility, so that should be a good thing. The problem is, supports generally love mobility and build mobility items because they have spells that they need to land. AM is kind of limited in the spells to land department, what with him hating magic and all that jazz. His ultimate is a decent nuke for kill securing and it can cancel channeling abilities and it's usually available in team fights with its 70 second cooldown.
Beyond that, well... his two passives are not great for supporting. In theory Mana Break is okay, but he is melee and rather squishy. Not a whole lot of mileage to get out of this one when supporting. It sounds decent for lane harassment against melee heroes at least. Spell Shield is probably even more useless because who wants to throw spells at a support Anti-Mage anyway? It can keep him alive in teamfights against AoE spells a little longer I guess. Not that it really matters.
I would probably start with Mana Break and grab Blink at level two, then max both of them before touching Spell Shield. Grabbing Mana Void at six is a no-brainer because it allows him to actually do something beyond right-clicking. He should start out in the lane and either pull or harass with Mana Break. I guess you can do that against ranged heroes when you get Blink.
Well he is not going to need a Blink Dagger or any other positional items. Unfortunately nukes and disables are rather expensive to build from items. Especially since Mana Break overrides Orb of Venom which would have been fantastic otherwise. I would probably go with either Eul's or Atos. He can blink initiate with Eul's provided that allies have some follow-up, or he can chase really well with Atos. Dagon is also an option if you need damage, and within the same price range. He could also build a Mekanism because he certainly has no mana problems. The problem with Mek is that then he really doesn't do anything with the blink ability (except instant delivery healing, whooo). Orchid and Hex are both a bit too greedy.
I guess Sange could be decent, but Atos is probably the better choice. A final option could be Necronomicon, since it kind of synergizes with Mana Break and Mana Void. Nevertheless, all of these items are rather expensive to build, and won't be available to a support AM in the early stages of the game. Another option is to just go full ward bitch, and maybe upgrade boots to Power Treads at some point. He can place wards in good locations with his blink at least. General support items like Urn of Shadows and Medallion of Courage could also be decent pickups. Mek and Urn are kind of good because support AM should be rather survivable because he has a blink, and he's not really a primary target.
Uh... well... I guess you can try harassing at lane as much as possible. You could roam, but since you have zero disables, the lane you roam to needs to provided that. Once you hit level 6 you can maybe look for potential ganks with your ultimate. Honestly since you are going to be very useless, a lot of the game plan depends on what other heroes can do. If there are some mana-intensive heroes, stick to them in teamfights to draw some focus. If for some obscure reason you can snowball from kills, Atos is probably the best choice to keep getting those kills.
I tried this a couple of times with very poor yet not unexpected results. You are basically just a blinking melee creep most of the game. It's also really hard to get levels unless you just stay in a lane and leech experience from a core. I tried to roam a bit but since AM's gank contribution is next to nothing, not much came out of that. In the first game I just bought wards and stuff, having literally nothing the entire game. In the second one I tried to be greedier, but failed to obtain an item once again. It is not a surprising in result in the least, considering how much early game Anti-Mage in general contributes.
In a typical teamfight you can get in a couple of attacks and hopefully you live long enough to get off a decent Mana Void. With his ult and a blink skill, AM is decent at stopping channeling ultimates like Fiend's Grip and Black Hole. So basically you get the contribution of a hard carry early game, and nothing in return. Which means your team will be playing 4 vs 5 all game. I predicted AM to be absolute trash as a support, and after attempting that a couple of times, it's safe to say that I was right. What a shock, huh?