I have the Verizon iPhone 4s, got it on launch day. It has a SIM card slot on the side. Does this mean I can use it overseas?
Out of the box, using the Verizon-branded SIM card that ought to have been pre-installed in your iPhone, you can roam in over 200 countries where Verizon has roaming partners. You'd have to enable Verizon's international roaming package on your account before you leave.
By default, the Verizon iPhone 4S is locked to Verizon's SIM card, so you won't be able to use a local SIM card in overseas countries. (However, for MOST of Verizon's world phones, you can apply to have the SIM lock removed after 60 days with an account in good standing.)
Keep in mind, Verizon has CDMA roaming agreements with companies in 20 or so countries (such as Canada), and in these countries Verizon hasn't bothered to establish any GSM-based roaming partnerships. So if you roam into any of these countries, you'll still be using CDMA (along with all the limitations that come with CDMA) instead of UMTS/HSPA.
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So I want to do the right thing.
I am wanting to sell it on Craigslist to upgrade to 32gb (i have a 16) Can I post it is a "world phone" and get more money for it?
It would be completely honest to say that your phone is a "world phone" exactly as it is today. However, you would have to note that it is locked to the Verizon network, and thus can only be used with Verizon for its home network, and is limited to Verizon's roaming partners for worldwide travel.
Do I call Verizon and have them "unlock it" or will it only be "unlocked" on my account or does it "travel" with the phone?
Also is there a fee to unlock?
After the phone is unlocked by authorized means, it will remain unlocked forever - it travels with the phone, not with the account. However, the unlock is only guaranteed to work for international roaming, not domestically. So basically, if you sell it to somebody else in the USA, they may still have trouble using it domestically with anybody other than Verizon.