Hopefully I'm posting this in the right area, just wanted some help before I continue. I'm playing survival mode (no cheats) and just tamed some cats that I had to use a boat to find. I want to bring them back to my house, but I'm gathering that they can't teleport that far. I tried boating a small distance and stopping on an island for them to teleport to, and one of them drowned out of my sight- none of them were able to teleport. I also want a horse, but I can't find horses or cats on the land mass I made my house on. Does this mean if I want to keep these animals I'd have to make a new house where I found them? Is there any way around this? Thanks.
You'll have to either ride the horse home, or lead it back with a leash. Across great distances, it can be a chore, but I've boated across whole oceans while leading them before. I've drug horses more than 6,000 blocks across plains, forest and mountain ranges.
Be forewarned: Mojang's leash mechanics are downright infuriating. If they would at least make a snapping sound effect when the leash breaks, one wouldn't have to nervously look back every 30 seconds hoping they're still leading their horse or horses.
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The Meaning of Life, the Universe, and Everything.
Cats and many other animals can be transported in a boat. The cat will have to enter the boat of its own will and will often do so even when you don't want them to. The cat will likely not enter the boat if you're already in it, BUT, if you swim out into the water near the boat, that will often entice the cat to get in the boat. Note that the cat will not leave the boat until you break it.
So I can confirm that I have to walk-backwards, especially around any Hills /elevation-changes, to make sure the Mob being towed by the Lead has time to walk-up, and /or drop-down, the Blocks (they Still quite often have to Break the Lead, so one tip is to carry-multiples, and watch the numerical indicator in the HotBar Slot like a hawk, not-just the Mob[s and of-course after about 2-3 Mobs, they Bump each-other enough that they tend to de-Lead - Break the Lead - faster]). Now, with other than Horse-types (Biggest thing we can attach a Lead to..?), we can If it's over-Water use a Boat, to Transport One at a time (which since it saves Food is a bonus, anyway, but they're technically-faster than Riding, Horse-types I think).
Later this Mechanic can be exploited again with at least one Mob by Lead'ing a Mule-or-Donkey, making a "flotilla" of "ship(s)" with extra items (since Slots, of Inv'y.-type shorter-term Storage). But they couldn't-Fit at all in a Boat (however, possibly because it's Water, they Tend to Not Break the Lead[s], so it's enough for me to look-behind as written here every 30 sec's. or so).
There may be a little-"Bug" of late (1.14.2, am currently Playing on) in which Dogs for-example "can't Teleport," like practically at all, and can't get-out of Water onto-Ice (often Drowning-underneath, though this might be the Puppies, somewhat-more [which used to Drown-Always in Water due to Hitboxes, before-1.14]). I end up having to go-back and walk them uber-slowly as they refuse to keep up with me (could just be Lag, on my end, too), and even then they seem to "stall out," so they've apparently become temporarily-unusable.
I'd had to Build 4-wide X 4 high (for Dismounting-and-Mounting without hitting my head, both-ways) Nether-side Nether Bases' interiors, to facilitate Nether Portaling of Horse-types. I don't recommend doing-this until those Portals have been Tested first and-guessed pretty carefully about safety on both ends (the time-consuming part is always Navigating them through the Nether, but that goes straight to Nether Navigation, generally, pretty quickly, and I use Markers of artificiality to distinguish from the natural Nether), As-for (not just a) Horse-type.
For whatever reason, I've had Horse-types Despawn, as of a few Updates ago, in any area smaller than about 4 X 4 (or about 3.33 Blocks, wasn't sure if the Fence Gates'd applied) both-directions sideways (they themselves are essentially 2 X 2 so this isn't very surprising to me). And /or they're Suffocating-dying (again, haven't tested lately due to previous losses being convincing-enough).