Here's a curiosity for you awesome rules junkies! Adjacent, in my mind, means "next to," but could also be read as "one square away." That being said, let's explore this thought process!

Exhibit A, and a familiar one at that:

(Special) Link Telepathically: Friendly characters within 4 squares can draw lines of fire and count range and squares from the square of any one friendly character within 4 squares of Tellus.

Exhibit B:

(Special) Personal Cloaking Device: When it's not your turn, lines of fire can't be drawn to Iron Man if he occupies hindering terrain or is adjacent to blocking terrain.

So my question, and one I've not seen discussed, is: Can we count squares of adjacency, remotely? I.E. Could IIM038 Iron Man be standing out in the open, and choose to count his adjacency square from a friendly within four squares of SLOSH048 Tellus, if said friendly is standing adjacent to blocking terrain?

Maybe it's a silly question with a simple answer, but some food for thought nonetheless.

No, because Iron Man is not adjacent to anything. If he was drawing lof to make a ranged attack against an enemy adjacent to Tellus, it would be legal because Iron man is not adjacent to the target. He's not adjacent to anything that Tellus is adjacent to.

Ahh I see what you did there, and what I mis-typed. Let me rephrase my question above.

AAA
AXA
AAA

Squares A are adjacent to square X. No other squares are adjacent to square X.

Some abilities/powers change what squares are considered to be adjacent for some purposes (see Giant Reach on the PAC) but they will always spell it out clearly. Tellus's power does nothing for adjacency.

I would say that just because ironman may use the Telepathic Link ability above to draw LOF and range from a remote friendly, or someone else draws it from him, the definition of 'adjacent' as it applies to ironman or other characters is still as per normal.

There are some abilities, namely a certain poison smoke cloud that I think Joker can use (forgot the name of it), that in affect extend adjacency, but it would have to do so in the wording of the ability, which Telepathic Link doesn't do.

That's my interpretation of things.

EDIT: Ah, I see VP already gave the correct answer. Glad to see I wasn't wrong on that.

Uh... no? The way you've worded things is a bit confusing so maybe I'm not getting the gist of what you're proposing. I sounds like you're asking if someone attacks IM in the open if he could use "Link Telepathically" and be considered as occupying/adjacent to hindering/blocking terrain. Since "Link Telepathically" and "Personal Cloaking Device" deal with two completely separate situations (attacking vs. defending) they do not interact in the way you have described.

Is counting 0 squares = adjacent? It's an interesting idea. But as far as I can tell the answer is an emphatic No.

From where you count squares does not matter when it comes to adjacency. The squares need to touch each other in order to be adjacent. Unless there is some kind of game effect (e.g. giant reach) that specifically states that it grants adjacency.

You seem to be the first to grasp the philosophy of the debate. While I believe you're correct in your argument, I had just never seen the question asked.

Incorrect. We, or at least I, understand your point, but the answer is the same. Telepathic Link doesn't say anything about providing the ability to remote your adjacency. It allows you to remote your Lof and range only.

Even if it could, as per your original post, it would still be a range of 1 from the remote character to the hindering terrain, and not 'adjacent = 0'.

Adjacent squares are 1 square away.

Adjacency is based on what things are physically next to each other, unless an effect specifically mentions otherwise. Since adjacency has nothing to do with counting squares, Tellus does nothing for adjacency.

EDIT

Being 1 square away doesn't make something adjacent, I meant that under normal circumstances, squares that are adjacent to something are also 1 square away from that something.

I got what you meant as well. I know using ranged combat in my example led you to believe that I didn't understand.

Enhancement and Empower figures would love it if things were adjacent to there own squares, but they are not.

The big problem here is this:
Doing these kinds of things is pretty much always a bad idea.
Take the rules literally for what they say and do not try to divine things from what you think they represent.

Except that Giant Reach will be able to use Tellus to stretch its strike-range.

Since giant reach has you draw LoF and count squares, Telepathy kicks in when doing that and ends up expanding the squares which can be adjacent further than normal.

For regular attacks you are spot on. No lof/square counting going on, so no telepathically extended melee attacks there.

The question has in fact come up many times before, because there are a lot of effects that care about adjcacency. Howevers, being within 1 square is definitely not sufficient for being "adjacent" as things such as walls and elevated terrain can make two squares non-adjacent even if they're next to each others on the map.