Will google accounts automatically update my friends addressbooks I was with Verizon Wireless when I had my HTC Eris (now due to issue with VZW and upgrading my phone I cancelled with VZW). I moved over to sprint and to a phone OS that shall not be named, but now I am on the verge of getting the Samsung Galaxy S4. During my switch, I did NOT keep my phone number and took a new number with Sprint. The problem is that my friends may still have my old number in their Google contacts and I am concerned that switching on the Galaxy S4 would cause Google to update my number to anyone who has my number in their Google contacts.

So my question is, if I link my Google account on to my new carrier/device, will Google update anyone who has my number in their Google contacts automatically?
NO. Their contact list (that is synced with the Google account) is based on the GMail contact list. It is a local copy; so any changes must be made from their side.

However, if they synced/merged that GMail contact to your Google Plus account, and you updated your contact information in Google Plus, it's still possible for them to know your new number.