Vampiric Touch + FS/FGS - Who gets the hit points from the damage?

Question

Separately from my other question about where to get the spell attack modifier value from when sharing a spell with Find/Greater Steed, but similar in situation.

Vampiric Touch:

On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.

Does the mount recover HP from this attack when it delivers it, or does the caster?

Relevant Rules Text;

PHB, Page 202; Rules of Magic -> Range: "Other spells, such as the shield spell, affect only you. These spells have a range of self."

PHB, Page 204; Rules of Magic -> Targets: "A typical spell requires you to pick one or more targets to be affected by the spell’s magic."

Vampiric Touch; Range -> Self

Valid Targets: Self. "Affect only you."

Conclusion; the attack roll is a feature granted by the spell cast on yourself, with its own separate targeting function, much like the natural weapons function of Alter Self.

Alternate conclusion; Vampiric Touch (and Alter Self; natural weapons) does nothing, because creatures other than self are not a valid target for any component of the spell.

The answer to the suggested and linked question was asked separately explicitly because of the spell text saying "you regain," as opposed to "Make a melee spell attack," without being preceded by "You." There is room, I feel, for the answers to not cleave the same way.

Answer 1

Vampiric Touch is not an eligible spell for Find Steed.

Find Steed requires that the spell targets only the caster, while the text of Vampiric Touch specifically mentions other targets (emphasis mine):

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, [...].

The Range entry of spells description does not correspond to the target(s) of the spell. As an example, consider the Haste spell: it has a range of 30 ft., it has only one target and the target can be the caster itself. Hence, it is a suitable spell for the Find Steed feature.

A DM can overcome this rule and decide that Vampiric Touch works with Find Steed.

Suppose that the DM rules otherwise and Vampiric Touch is an eligible spell for affecting also the mount, under the rules of Find Steed¹. Then, the description of the spell implies that the attacker, who is also the caster, drains the HPs (emphases mine):

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.

There are two interpretations here.

• the mount is the attacker but it is not the caster: the drained HPs are absorbed by the caster, i.e. the mount acts as a "healing channel" for the caster for successful attacks.
• the mount is the attacker and it is considered also the caster, for the purpose of Vampiric Touch: the drained HPs are absorbed by the mount.

The DM has hence to adopt a ruling and decide the interaction between these two spells.

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¹ See this answer of mine for some discussion about the eligibility of Vampiric Touch under Find Steed.

Answer 2

Vampiric Touch cannot be shared with your steed

As on your other recent question, this whole question is based on a misapprehension: That Vampiric Touch is eligible for sharing with your mount. Vampiric Touch has a range of Self, but the target also includes any creatures you touch, not just you:

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt.

The spell does not target only you, so it's not eligible to be shared with your steed.

As a rule, if the spell, by any means:

1. Grants you a special (typically spell) attack (e.g. Vampiric Touch)
2. Includes an attack (e.g. Booming Blade)
3. Triggers a saving throw targeting anyone else

then it's not a spell targeting "only you", because the spell itself is responsible for that attack or save. Conveniently, this means you never need to worry about the attack roll or save DC the steed should use; if the spell allows for an attack/triggers a save, the steed can't use it.

If the Range entry alone defined something as "targeting only you", your mount could make Wishes when you do, and I'm fairly sure no DM is going to let you use your mount to make consequence-free Wishes.