This must be explored during the campaign and is ultimately the DM's call. Artifacts are a fickle and unpredictable lot, and their successful use will depend greatly on if the DM is trying to Gygax the PCs into hilarious, sooner-than-instant deaths.1 That said, were it my campaign, based on the Dungeons and Dragons 3.5 description of the item, the effect of one spheres of annihilation touching another is that
In Dungeons and Dragons 3.5 the sphere of annihilation (DMG 279) (minor artifact; 0 lbs.) says
A sphere of annihilation is a globe of absolute blackness, a ball of nothingness 2 feet in diameter. The object is actually a hole in the continuity of the multiverse. Any matter that comes in contact with a sphere is instantly sucked into the void, gone, and utterly destroyed. Only the direct intervention of a deity can restore an annihilated character.
A sphere of annihilation is static, resting in some spot as if it were a normal hole....
I'm neither physicist nor wizard, but, despite the initial reference to the sphere as an object, I believe that a "hole in the continuity of the multiverse" is not composed of what either profession would classify as matter even in D&D 3.5 terms. Thus by its own definition two spheres touching does nothing.2 I'd even argue that two spheres can't occupy the same place at the same time, that when attempting to move one sphere through another stationary sphere the moving sphere stops at the stationary sphere. This non-artificer-and-non-physicist would then continue arguing from ignorance that one simply can't put one continuity hole inside another continuity hole.3 I can, however, understand a competing theory wherein two (or more!) spheres would remain distinct while harmlessly overlapping, and, if true, the mind boggles at the potential for humor and danger.
This assessment jibes with the given--and apparently exhaustive--list of ways to interact with a sphere that don't result in annihilation as that list makes no mention of one sphere's impact on another sphere.
Any DM whose campaign contains madness sufficient to warrant his PCs attempting to weaponize multiple spheres of annihilation, therefore forcing them to worry about crossing the spheres--so to speak--, is likely to have something more... significant happen when spheres meet, if only because, well, it sounds like that kind of campaign.
- A la the classic Tomb of Horrors.
- The Example Negative Plane Site: Voidstone Field (DMG 157) gives one possible source for a sphere of annihilation, although this seems unlikely given the sphere's description later in the text.
- Cf. the portable hole (DMG 264) (20,000 gp; 0 lbs.), which is perfectly comfortable nesting inside another portable hole, but this item isn't so much a hole as a method of transportation to a specific (and--barring a Bag World-style scenario--distinct) demiplane.