How many actions to deliver Vampiric Touch multiple times through familiar?

Question

In public play, I have seen multiple wizards cast Vampiric Touch to deliver the spell through their familiar. I am curious than, how it works in terms of the action economy.

Vampiric Touch, PHB pg 285

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.

Find Familiar, PHB pg

Finally, when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its reaction to deliver the spell when you cast it. If the spell requires an attack roll, you use your attack modifier for the roll.

Does this mean I can cast Vampiric Touch once, and the familiar can deliver it round after round as a reaction, while I continue concentrating, avoiding the need for me to use an action? If not, how does it work, and do I need to "recharge" the familiar?

Answer 1

The first issue is that vampiric touch isn't a “touch” range spell, so it can't be delivered by a familiar anyway.

But let's ignore that for a minute and look at how the ability would work, if could work.

The most important limit on this ability is that your familiar can only deliver a spell as if it had cast it. Everything else about how the spell works is still as if you had cast it, with only the way it's delivered changing:

when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell

Once it's delivered, the familiar has nothing further to do with the spell. So after delivery, you're still in control of the delivered spell, and it still requires your personal resources to do anything in its description.

(This stuff is likely part of why “self” range spells are disallowed — they would complicate an otherwise simple ability — though I can think of many other ways it would be complicated to allow familiars to “deliver” self-range spells.)

Answer 2

You can't do it.

You can only cast spells through your familiar that have a range of touch. Vampiric Touch has a range of self.