Oracle Text

Counter target spell. Search its controller's graveyard, hand, and library for all cards with the same name as that spell and exile them. Then that player shuffles their library.

Card Rulings

5/1/2008 Counterbore has no effect on cards on the battlefield that have the same name as the targeted spell.
5/1/2008 The cards you’re searching for must be found if they’re in the graveyard, because that’s a zone everyone can see. Finding those cards in the hand and library is optional, though.
5/1/2008 In most cases, Counterbore will exile the targeted spell. Its first sentence counters the spell, which puts it into its owner’s graveyard. Its second sentence then removes it from the graveyard. However, there are some exceptions to this, as listed below.
5/1/2008 If the spell’s controller isn’t the same as its owner (due to Commandeer, for example), it won’t be exiled. The spell is countered and put into its owner’s graveyard. Then the spell’s controller’s graveyard, hand, and library are searched.
5/1/2008 If the targeted spell can’t be countered (it’s Vexing Shusher, for example), that spell will remain on the stack. Counterbore will continue to resolve. You still get to search for and exile all other cards with that name.