What happens to active spells on a black pudding when it splits?

Question

Bob the wizard and his chums have encountered a black pudding and Bob has cast Slow on it to give him some time to run for it. However, helpfully, the next round the parties tank, Kevin the Barbarian, smacks the pudding with his greatsword and splits the pudding in two.

What happens to the slow spell? The Split info for the pudding is minimal.

Split (Ex) Slashing and piercing weapons deal no damage to a black pudding. Instead, the creature splits into two identical puddings, each with half of the original's current hit points (round down). A pudding with 10 hit points or less cannot be further split and dies if reduced to 0 hit points.

Are both puddings still affected by the slow spell?

Answer 1

Both Puddings Are Slowed

In this case, both puddings should be slowed. This isn't specific to being slowed, it should be true of any condition or spell effect.

Spells and conditions have definite points at which they terminate. A spell doesn't end unless a certain condition is met (the duration is met, counterspell, etc.) - and the Split ability isn't one of them.

Detailed Explanation

I'm going to walk through this inductively, since there isn't a single rule to reference:

Both puddings are either afflicted with the spell or condition, or neither is. The text of the black pudding's ability says (emphasis mine):

Split (Ex) Slashing and piercing weapons deal no damage to a black pudding. Instead, the creature splits into two identical puddings, each with half of the original's current hit points (round down). A pudding with 10 hit points or less cannot be further split and dies if reduced to 0 hit points.

If one of the new puddings is slowed, but the other isn't, than they aren't identical.

Both puddings must be slowed, since the Slow spell hasn't ended yet. Two possibilities remain: either both puddings are slowed, or neither is.

Slow has a duration of 1 round per level. Without some other effect that removes slow (such as Haste), it stays until the duration is met. The black pudding's Split ability does not explicitly remove any magical effects or conditions.

Limitations This interpretation follows from the rules text, but relies on the non-existence of a clarifying rule. If someone does find a specific rule that governs this, it would be authoritative.

Answer 2

Neither pudding is slowed

As counter-intuitive as it is, each pudding is free of any conditions suffered by the parent, as each is a new creature:

Split (Ex) Slashing and piercing weapons deal no damage to a black pudding. Instead, the creature splits into two identical puddings, each with half of the original's current hit points (round down). A pudding with 10 hit points or less cannot be further split and dies if reduced to 0 hit points.

There are three puddings involved, as identified by the ability: the original, and two (necessarily new) identical puddings. Any effects suffered by the original are still attached to that original creature, but since it no longer exists, the spell effect ends due to no longer having its original target to continue affecting.

(This is something that I would personally house-rule to the contrary, though, since it makes more sense to me, as a fiction-driven GM, to have the spell persist on the two new puddings.)