Unicorn horns

[ladyramkin2000]

No: HPFGUIDX 90547

Entropy quoted from The Forbidden Forest chapter (Pg 258 in US 
edition):
"Harry Potter, do you know what unicorn blood is used for?"
"No" said Harry, startled by the odd question "We've only used the 
horn and tail hair in Potions".
Thanks, Entrophy, that is exactly the bit I was trying to remember. 
But I'm still puzzled as to how they obtain the unicorn's horn 
without harming the animal.  Do unicorns shed their horns? Or are the 
horns removed after the creature has died naturally?  I imagine 
unicorns must be pretty rare, even in the WW so how do they obtain 
sufficient horns for school-children to use in potion making?

Sylvia