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The description of the Mordenkainen's faithful hound spell says, in part:

You conjure a phantom watchdog in an unoccupied space that you can see within range, where it remains for the duration, until you dismiss it as an action, or until you move more than 100 feet away from it.

If I were to cast Mordenkainen's faithful hound to conjure the hound on a wagon, or on Tenser's floating disk, would the hound then be able to follow me around and remain active for it's 8 hour duration?

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A surface isn't good enough, it's only mobile if you cast it on a mobile space

The spell neither requires nor interacts with surfaces; you can cast the spell in the formless void of the Plane of Air or 20 feet off a cliff or 200 feet under water in the middle of the ocean, it makes no difference.

Spaces are, however, mobile. Many settings include a planetary cosmology, for example, so the spaces one mostly deals with orbit the setting's Sun or Suns much like a point on the surface of the Earth. Moreover, large vehicles like sailing ships or spacecraft are often mapped out with spaces corresponding to the vehicle rather than the 'ground'. The hound would move along with both kinds of moving spaces just fine.

While there's no way Tenser's floating disk gets its own spaces rather than occupying some/one, a wagon might be big enough to get spaces, though it's unlikely. If it did, this plan could almost work, but it doesn't let the hound change spaces so as soon you moved to a situation where that vehicle was supposed to be following you around (i.e. you aren't in the vehicle; it isn't serving as a location) it should occupy rather than have spaces, and the spell would no longer work the way you wanted (though what actually happens in such a case, much like what happens if the grid alignment changes between scenes with a more traditional space, is not specified in the rules).

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  • \$\begingroup\$ Suppose a pixie (Tiny: occupies a 2.5' x 2.5' space) lands on an Floating Disc (3 feet in diameter, 3 feet above the ground). A second pixie, hostile to the first, attempts to walk under the floating disc. This is impossible because the Floating disc is not its own space, it and the pixie on it are occupying the same space on the ground that the second pixie is trying to enter? \$\endgroup\$
    – Kirt
    Sep 6, 2020 at 16:16
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    \$\begingroup\$ @Kirt The game does not handle vertical displacement or Tiny creatures well. A DM running a game regularly involving conflicts between flying or tiny creatures is well advised to come up with their own rules for that purpose-- the default ones (under which the answer is the Pixie can go in just fine cause it's Tiny, and tiny creatures control less than 1 space, but it can't enter a region of that space corresponding to the column which is controlled by the pixie) don't work if you want balance or things to be close to how you expect for the intended genre. \$\endgroup\$ Sep 6, 2020 at 17:21
  • \$\begingroup\$ @Kirt also remember that a Pixie does not control a 2.5x2.5 space-- it controls 2.5x2.5 worth of area around it; the rules for the hound require the 'playing on a grid' optional rule which is a different sort of space. \$\endgroup\$ Sep 6, 2020 at 17:24
  • \$\begingroup\$ This feels like "Ask your DM", as none I know would make the game world work by such arbitrary definitions of 'space'. \$\endgroup\$
    – Weckar E.
    Sep 6, 2020 at 18:19
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    \$\begingroup\$ This answer would benefit from a citation describing the difference between spaces and surfaces. Is this a rule? \$\endgroup\$ Jan 1, 2022 at 18:45
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It's not clear by the written rules. But it's a reasonable thought.

So, as the spell is written it doesn't move at all, which begs the question, what happens if my world is on a moving planet? Will the hound instantly fly away and disappear into space?

Since that doesn't make for a functional spell at all it's quite obvious the hound is meant to stay still in relation to some frame of reference. Which is normally just the ground you are standing on.

But clearly, in D&D we sometimes have fights in places that are moving in relation to the world. Could be a carriage, a ship, or whatever. Does the hound remain stationary in relation to the ground there, meaning it's displaced from where we are standing?

I think it's a ruling many DMs would make that the hound stays anchored to the surface it was summoned in. The other answer as of now, explains this as being due to that hypothetical ship or whatnot having its own mobile 'space' (which I think refers to it having its own grid and that objects placed in it remain stationary in relation to each other).

I think this raises some issues when you have multiple representations of spaces. For instance, you could have a grid for your ship and another battle map where your ship is a miniature and other ships and creatures exist there as well. There, your hound could interact with a hostile creature next to your ship, even if it's not in the mobile space represented on your ship's grid (let's say it only goes up to the border of your ship). So we are forced to recognize the hound as moving through a space.

Ruling that the hound can remain stationary in relation to any surface it's summoned on seems quite reasonable.

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