Question: In my story, there is a character that is capable of using magic or an ability that allows them to "teleport" as long as they are in contact with the ground or the area that they want to use it on with at least one hand.

For example, in the middle of a circular arena 100m in diameter, as long as they are touching the floor (with a hand), they can teleport anywhere as long as it is "connected" or still physically part of the arena (which means that any floating rocks won't count, and they wouldn't be able to use it to get away from the arena in the case that it is floating).

What limitations can be set on it to avoid being too powerful, and with limitations in mind (or not), what would be the best type of magic/ability to use with it? (disregarding earth magic/manipulation)

My thoughts were to limit it to 75-100m and only usable every second or two, and to be used with wind magic mainly (if mist or fog can be made using wind magic).

Answer: 
Instead of true teleportation, have them move within the ground as if it were not solid. They can "merge" with it and move around really fast - maybe so fast that for practical purposes, it is much the same as teleporting.

The advantage of this is that it prevents the user from abusing this power. For example, in the teleportation model you propose, one could teleport from an arena to a floating island if a rope connects those. The user could throw a rope with a hook on a floating island, and then they could teleport at will. But if they have to physically move through the ground, this prevents them from moving through ropes, chains, or other narrow passages because their body will not fit through the passage.

An example of such "teleportation" is the [Inkling in Super Smash Bros. Ultimate](https://www.ssbwiki.com/Inkling_(SSBU)). She is able to become a puddle of splashing ink and move around the scenario. In this manner she can avoid most attacks because they will pass over her, and she can move extremely fast from one point to another, but this does not allow her to move from one floating island to another.

Another example is Zetsu, from the animé Naruto. This guy is able to practically "fly" inside rock and earth. This allows him to disappear from one place and appear in other really fast, but also does not allow him to move from the ground to a floating place (and there have been floating places in the animé).

[![Zetsu, a character from the animé Naruto, merging with the ground.](https://i.stack.imgur.com/iXmBK.gif)](https://i.stack.imgur.com/iXmBK.gif)

And finally there is King Bumi in Avatar: the last Airbender. This technique shows in the few first and few last seconds of [this video](https://www.youtube.com/watch?v=PTu5t2nhOrw).
One of the easy ways to eliminate the more extreme abuses is a line-of-sight limitation. You can only teleport to a location if you can currently see it. That puts a hard cap on the range of the effect, and introduces opportunities for opponents to disrupt it (fight indoors, obscure their vision, etc). Teleporting somewhere you can't see isn't a really good idea anyway, because you have no idea if the laws of physics will even permit you to exist in that space (ending up inside a solid object would be game over for you).

For an extra twist, you can limit how close you arrive to your target point to be dependent on how clearly you can see that point. For example, stick out your thumb and hold it at arm's length, covering up your target. The area of your thumbnail represents the size of the area in which you might end up. When teleporting across the room, that area is only a few square inches so accuracy isn't really an issue. Teleporting to that hill far in the distance could be a problem, though. That same thumbnail-sized area is bigger than the apparent size of the hill, so you might miss your target completely and end up somewhere undesirable.

Any sort of teleportation is going to be rather overpowered in combat, simply because it lets you evade attacks nearly perfectly. The most straightforward way to reign in the usefulness would be to make teleportation not an instantaneous process. The caster has to focus/concentrate/channel for a period of time before teleporting. This prevents it from being used *reactively*, which is where most of its overpowered nature comes from. It also leaves your caster vulnerable just before they teleport, which means it has to be used much more strategically. Great for sneak attacks or initiating fights but once the fight starts, you can't fight invincibly like Nightcrawler in X-Men United.

You can even incorporate this into the lore if you want. Teleportation is a form of shadow magic. The caster channels their magic to send their shadow to a distant target location. Once the shadow reaches the destination, the caster will suddenly find themselves there as well (like how you can travel to the other room and turn on the light to make your shadow appear at *your* location, only it works the other way around). The shadow travels at a certain speed, say, 10x the speed of the caster. The caster would then have to channel for some brief minimum length of time *plus* however long it takes for the shadow to travel from A to B. That won't completely preclude its use as a combat escape mechanism, but will require your character to earn themselves enough breathing room to complete the cast.