A PC uses the spell shapechange to assume the form of a deepspawn (Monster Compendium: Monsters of Faerûn 32–3).
Can the PC use the deepspawn's spawn ability? If so, are such spawn forevermore under the PC's control?
A creature that uses an effect like the 9th-level Sor/Wiz spell shapechange [trans] (Player's Handbook 277–8) to assume the form of a deepspawn may or may not gain the deepspawn's spawn ability, depending on the deepspawn that's being used and the DM's ruling.
Monstrous Compendium: Monsters of Faerûn for Dungeons & Dragons, Third Edition doesn't classify the spawn ability of its deepspawn (32–3). This makes the ability by default a natural ability (PH 180), and this means that for a creature that assumes deepspawn form to gain the natural ability spawn the DM must rule that the natural ability spawn is a "gross physical quality" as per the 2nd-level Sor/Wiz spell alter self (PH 197)1. This reader suspects many DMs won't rule this way, but maybe the DM's in a good mood or it's the end of the campaign so it doesn't matter or something. In that case, here's that ability:
By some unexplained, natural means, deepspawn can grow and give birth to any creature native to the Material Plane that it has ever devoured (not outsiders, elementals, undead, or other dual-dimensional creatures). A spawn has the same type, natural attacks, magical abilities, alignment, and intelligence as the creature devoured by the deepspawn, and it retains learned abilities (class abilities, skills, and feats) as well as some dim memory of its former existence. A spawn grows in 1d4 days within the deepspawn's body, then emerges fully formed and ready for immediate action. Spawn are completely loyal to the deepspawn that formed them, and cannot be made to attack their "parent" even by magical means. (Monstrous Compendium: Monsters of Faerûn 33)
(Emphases mine.) If a generous DM rules that the creature that's assumed deepspawn form keeps in its assumed form, I suppose,—I struggle for the word here—a record of every creature it's ever eaten no matter its current form, then, after 1d4 days in deepspawn form, that creature can birth a creature that it ate once according to the above description.2,3 Note that the shapechange spell has a duration of 10 min. per level, so while it's far from impossible to apply to a shapechange spell the benefit of the metamagic feat Persistent Spell (Complete Arcane 81), it seems—to this reader, anyway—excessive to do so solely to breed minions!4 Further, once the creature assumes a form other than that of a deepspawn, the birthing deepspawn doesn't exist.5,6 The spawn is then essentially free-willed, possesses "some dim memory of its former existence," and reeks of plot.
Lost Empires of Faerûn for Dungeons & Dragons 3.5 classifies the spawn ability of its deepspawn (166–8) as an extraordinary ability, and a creature that uses a shapechange effect gains the extraordinary abilities of an assumed form. The ability gained is this:
A deepspawn is usually encountered with one to three of its spawnmonsters of CR 4 to 6. Spawn are fanatically loyal to the deepspawn that spawned them and willingly fight to the death to defend it. To determine what kind of spawn accompanies any given deepspawn, roll d% [on an omitted table.] A deepspawn can spawn only creatures identical to those it has physically consumed. [N.b. As opposed to mentally or spiritually consumed, I guess?] Each spawn possesses even the learned abilities (such as class level, skills, and spells known) of the original but retains only dim memories of its former life. Only Large or smaller corporeal, living creatures native to the Material Plane can be spawned. After spawning, a deepspawn must wait 4d6 days before doing so again. (167–8)
(Emphases mine.) A creature that assumes this deepspawn form can take a standard action to use the extraordinary ability spawn immediately upon assuming deepspawn form! Again, eating and tracking the monsters that can be spawned is a thing, but, unlike the Monsters of Faerûn deepspawn that can birth a tarrasque, the size limitations above severely restrict what a newfangled deepspawn can birth. Further, like the original, the disappearance of the birthing deepspawn frees the spawn. (The Third Edition footnotes apply pretty much equally here, too.)
If the goal is increasing the monster population, I suggest also investigating the 4th-level Sor/Wiz spell Halaster's fetch I [conj] (City of Splendors: Waterdeep 153) et al. While those spells aren't as versatile and don't spawn minions as loyal, those spells are much easier to use—and far less squicky—if all you need is creatures to populate your dungeon.
1 Feel free at this point to make your own gross pun.
2 If the DM rules that the creature that's assumed deepspawn form does not keep such a record, the creature that's assumed deepspawn form will need some monsters on hand to consume before he can birth. Good luck and bon appétit!
3 For more means of eking out benefits from eating one's foes (at least, this player hopes they're foes!), see this 3.5 question and this Pathfinder question.
4 If a creature can employ persistent shapechange, the creature can probably more quickly produce minions than by popping one out every 1d4 (or 4d6) days!
5 This DM would rule that the creature that's assumed deepspawn form must remain in deepspawn from to be able to birth to more spawn, counting time spent only in that form toward the spawn ability's duration. With that in mind, the shapechanged creature may struggle to make friends: even high-level adventurers—who are typically a pretty kooky bunch already—may balk at camping alongside a perpetually pregnant tentacle monster. Just sayin'.
6 The DM must decide when a creature assumes form A then assumes form B then assumes once more form A if form A is the same form A that was assumed previously. This DM gravitates toward yes as that prevents some shenanigans like a creature assuming the same yet subtly different form repeatedly to reuse a creature's limited-use abilities like the 1/year supernatural ability wish of the zodar (Fiend Folio 199), but that ruling does give the creature that births monsters in deepspawn form an advantage.
RAW "You gain all extraordinary and supernatural abilities [...] of the assumed form" so you would be able to summon them. Whether or not you control them after the form is lost is a left to GM discretion but the most likely responses will be they disappear as the supernatural magic that created them is no longer present, or they become uncontrolled NPC's and eat your faces because the thing that spawned them is no longer around to reign them in.