Has Ichigo's soul cutter existed before him? I have a problem with the manga Bleach. When Ichigo became shinigami for the first time, it was said that his soul cutter is so big because of his spiritual powers, which means that your soul cutter is a reflection of that. But when they go to soul society it is clearly hinted that the shinigamis there choose their soul cutters and that the soul cutters they have have existed for generations before them. Can someone help explain this to me?
This answer can only be explained with a big spoiler. Those who hasn't read Bleach till the latest chapter and wish not to be spoiled might better avoid reading this altogether.

Note: the way I understand it, there are 3 questions you asked.


The correlation between spiritual powers and Zanpakutou's size.
Zanpakutou existed even before the Shinigami.
Did Ichigo's Zanpakutou existed before him.


Answer to Question 1

A Shinigami's Zanpakutou's (soul cutter in English dub) size reflects the Shinigami's spiritual powers. The more spiritual power it unleashed, the bigger it becomes. This is generally true.

Example 1

Renji's Zanpakutou's normal shape is a normal Katana. When the released into Shikai form (Zabimaru), it unleash more spiritual power and its shape got bigger. It gets even bigger when Renji is in Bankai state (Hihio Zabimaru) and even his body is covered by his power in form of the furry cloak.

Example 2

Zaraki Kenpachi's Zanpakutou's normal form is a long katana with chipped blade. When released into shikai, his Zanpakutou changed form into a chopping axe shape.

Example 3

Madarame Ikkaku's Zanpakutou's normal form is a normal katana. It's shikai form (Houzukimaru) is a spear, it's bankai form (Ryuumon Houzukimaru) is a huge blades linked with chain.

Example 4

Soi Fon's Zanpakutou is a short katana. Shikai form changed it into a smaller shape, but it's bankai changed it into a big rocket launcher like thing. Notice how its shikai form is smaller that its normal form, unlike the previous two examples, which is why I said that Zanpakutou's size reflects the spiritual power is generall true. Also, so far she has never been see using her Zanpakutou in its normal, unreleased state.

Another exception to this is Kurosaki Ichigo. Kurosaki Ichigo's Zanpakutou is always in its shikai form. But its bankai form actually made the blade smaller, and denser, unlike bankai in general, which was noted by Kuchiki Byakuya during their fight. Byakuya also said that he don't believe that such a small sword (compared to Ichigo's shikai and bankai in general) can be his bankai.

Edit:
As mentioned by Ryan and Memor-X, Zanpakutou's size can be controlled. This was mentioned by Kurosaki Isshin to Grand Fisher, that if Zanpakutou's size is not controlled, those with huge Spiritual Power like the Captains, would literally have skyscrapers on their hands. 

Answer to Question 2

Normally, a shinigami is given an Asauchi, a blank Zanpakutou created by the creator of Asauchi, Ouetsu Nimaiya. This blank Zanpakutou will develop along with its wielder and make itself unique. This is how Shinigami normally got their Zanpakutou. Therefore, since all Zanpakutou (with the exception of Zangetsu) was an Asauchi, it can be said that it existed generations before the current generation of Shinigami).

Answer to Question 3

Kurosaki Ichigo's Zanpakutou, Zangetsu, is special since Ichigo is a son of Shinigami and Quincy. His father, Kurosaki Isshin is a Shinigami and his mother was a Quincy. What he used to fight until his fight with Aizen Sousuke where he lost his "Shinigami" powers due to the use of Final Getsuga Tenshou, was later revealed to be his Quincy powers. It was confirmed by Zangetsu (old man form) himself. Zangetsu also said that the reason his figure is so similar to that of Ywach was because Ichigo also has a Quincy blood in him. His power is in his blood, thus it can be said that his Zanpakutou existed from the very moment he was born.