According to the terms and conditions, its neither:

You can terminate your Plan at any time prior to your next Billing Due Date by emailing us at support@2degreesbroadband.co.nzor by calling us on 0800 022 022. You will still be liable for any Charges incurred up to that Billing Due Date, including any usage-based Charges (such as toll calls and/or excess broadband data) and any applicable early termination or failure to return modem Charges.

 

 

1. You can terminate your Add-On Services at any time prior to your next Billing Due Date by emailing us at support@2degreesbroadband.co.nz, calling us on 0800 022 022, or via Your 2degrees Broadband. You will still be liable for any Charges incurred up to that Billing Due Date including any usage-based Charges (such as toll calls and/or excess broadband data).

The dates are different now with the new billing system as you now pay after the start of the billing period for that period, not before it looks like. So my interpretation now, you should contact them before the end of your billing period/month, so it doesn't roll-over into a new one, and to be safe, put an end date of a day or two before the end of the period. However, only do that if you are your new/replacement broadband is on a different port. If you are doing the same port, then contact new provider with the date before end of billing period, then contact 2Degrees.

I've been meaning to move away from them for a few months now but been lazy. The current issues with broadband changeovers have pushed me to be active and change providers.

Edit: This assumes you are already out of contract. To do this cleanly, you may need to pay for an additional month at the end of your contact and terminate in that extra month.