Subject: Did comets bring all the water to Earth?

I've been reading about the panspermia hypothesis (life was brought to 
Earth by comets or asteroids) when it struck me - where does the water on 
Earth come from? Several authors say that Earth was too hot for water in 
the beginning, but they don't say where the water in the oceans came from. 
Was all the water on Earth brought here by comets? If so, does this 
strengthen the panspermia hypothesis?  Side question: does a planet need an 
atmosphere to keep water; would water boil off a planet with no atmosphere? 
Thanks for your answer!

Re: Did comets bring all the water to Earth?