We are all going to need to get our heads around how a franchise system works. (Reading the full NECA report is homework I have yet to do ...)

As I understand it, for services that cross the boundary  of the franchised area, I think the rules are:
- a franchised service can extend outside its home area, just needs that part of the service registrering with the Traffic Commissioner. The route, timetable and fares etc for the section outside the franchised area are still determined under the terms franchising scheme, so most likely will be decided by the franchising LTA. (This is common around the edges of TfL.) 
- a non-franchised service can operate into the franchised area if the franchising LTA decides it complements services in the franchised area, as per Malarkeyss message.  (This is common around the edges of TfGM, such as services to Manchester from Lancashire, etc. I don't think there is currently any material franchised operation crossing the boundary of TfGM.)

Around the borders of the NECA area, assuming the franchise is going to cover the whole region, I think it will be like this:
- the services into Berwick from Scotland will be permit operations.
- the services into Carlisle and Alston will surely be franchised?  (The route of 685 is about 80% in NECA; I don't think there is anything to stop the franchised operator having buses based outside the NECA area, and for that matter, in principle nothing to prevent a permit operation being run from a depot in the franchised area.)
- the services between County Durham and Tees Valley will be franchised UNLESS NECA for some reason deliberately leaves room for them so they are "complementary" and they area able to run "commercially". But remember that even though much of the current Arriva services are not under a DCC subsidy contract, they are almost certainly only "commerically viable" because of the BSOG+ paid to them by DfT. I think that under the franchising all that funding will transfer to NECA for them to choose how to spend; plus NECA fares will apply (with the funding of the national farecap also transferring from DfT to NECA). 

Re Weardale and Stanley Travel: the bus services will become subject to the franchise system. Plenty of them are already, effectively, as bar a few they aready run under DCC contracts. It will be interesting to see how all this turns out for their considerable school contract operations.