When you place an order with your new isp, the gaining isp will contact the losing isp and make the arrangements. Once the transfer is complete you final bill will be made out (if applicable) and your account closed. Or this is how it should be. Making contact with the losing isp can cause issues and sometimes mis communications can end up with a chargeable cease instead of a seamless migration.
Your new provider will inform us of when they are taking over the line. The final fees against your account (if applicable) will be calculated 21 days after your services migrate to your new provider.
