A Zan spirit can be born even without the Asauchi, but the Asauchi is needed to pour onto it the Zan that is inside the Shinigami, allowing to manifest their Shikais and Bankais.
You could say that Asauchi is used as a frame, upon which they build their Inner Zan Spirits. Of course, you can still build it without a frame, but it will be way harder that way.
The whole Zanpakuto/Asauchi thing is really Messed up in my view.
For instance, all the girls that greated Ichigo and renji in Ouetsu's palace are Zanpakutos, how is this possible? Who is their Shinigami?
Also the Asauchis have legs and arms, and they have emotion (anger). In other words they are not merely swords, they are beings with rudimentary functionality and almost no personality.
The Shinigami's Reiatsu molds them and imbues them with personality and intellect. If this is so, then Rukia's sword could not be the source of Ichigo's Asauchi, because her Asauchi has already become Sode no Shirayuki/Mai
Just a couple of thoughts on the chapter and the discussion so far:
1. Ichigo has always been unique among the shinigami, both in his origins and in how he has acquired power. I don't think we should try to twist the usual method to fit his unique circumstances. After all, to reach Ichigo's level of power usually takes centuries.
2. Why was there the abrupt change in Unohana's personality, when she and Zaraki began their training? She's been presented as a calm and unemotional person this entire time, and now she's been unleashed as a raging beast. Is it possible that her capacity for violence was locked or sealed inside of her? If it was, that would explain why she didn't participate in the battle, for fear of what unlocking that ability would do.
3. Maybe what would be killed would either be Zaraki if he can't overcome the violent Unohana, or the remains of the violent Unohana, and nothing would be left except the relatively peaceful leader of the 4th division.
EDIT: one more thought, Zaraki isn't a killer. He enjoys the battle, not killing. That's why he has the bells in his hair, wears an eyepatch limiter, and refused to listen to his zanpakuto. He doesn't care if his opponent dies from the battle, but he doesn't finish off his opponent without severe provocation. From what we've heard about Unohana in the latest chapter, she was a killer. Hopefully, she can turn Zaraki into a killer as well, because I don't think he'd survive another battle with the Quincy if he isn't.
The sword afterall looks exactly the same as hers it's just oversized. She gave him her powers = she lent him her sword.
Also, i take a bet that each and every one of those girls are Oetsu's Zanpaktous. Wy "The number one Zanpaktou Maker" would not be able to create a few Zanpaktous, and pick and choose the one he feels like fighting with?
The Zanpakutou's name might very well be the imprinting code, that makes the Ausachi become a certain Zan. It's possible that naturally it's always an Ausachi until the code is used and when the Zan is recalled, it becomes a normal Asauchi again. In short, the Asauchi in the Sword, isn't the same as the one in the Shinigami, especially seeing as Urahara reduced Ichigo's Asauchi to nothing more than a handle, yet Zangetsu could still be called out in his full form.
I have a feeling Unohana's zanpakuto is multiple personality like her, the healing side is a big goofy flying sting ray but her real original side must be something so much deadlier, Im guessing almost like Ichigo and Yamamoto where everything is condensed into the blade for a more powerful sword etc. Zaraki better learn his swords name by the end of all this! At least to a point that his blade starts repairing itself from all the cracks etc.
I disagree with the assumption that Ichigo's bankai can be stolen. The bankai's that were stolen thus far are only ones that have had their full potential shown. IE, you couldn't steal yammy's bankai until they saw it's true powers. The problem is, Ichigo loves to go bankai, and use it for it's speed/strength boost but.. to be frank:
I'm not eve sure Ichigo knows wtf his bankai *really* does, therefore, it cannot be stolen.
This chapter burn my heart... hope both of them to live...