Here we go:

Northumberland and Tyne & Wear
In Northumberland children aged 5 and under 14 are charged at a discounted fare.

In Tyne & Wear, Under 16s with a valid Nexus Under 16 Card will be able to travel at a flat 60p Single/£1.10 day ticket CAT on local buses from the commencement to the termination of normal daytime services (not valid on night).

County Durham & Darlington
Children aged 5 and under 14 are charged a discounted fare for any journey starting or finishing in County Durham.

Within the Darlington Borough boundary children aged 5 and under 16 are charged a discounted fare. Please note that for any through journey crossing the boundary from Darlington into Durham, Tees Valley, Tyne and Wear or North Yorkshire the restriction for child fares reverts back to aged from 5 to under 14.

Tees Valley (Stockton, Middlesbrough and Redcar & Cleveland)
Children aged 5 and under 16 are charged a discounted fare wholly within the Tees Valley area. Discounted fare on cross-boundary journeys, i.e. to points beyond the local boundaries, are available only to children aged 5 and under 14.

North Yorkshire
Children aged 5 and under 14 are charged a discounted fare for any journey starting or finishing in North Yorkshire.