As Tummyman has suggested
Property ownership is set in the deed, as in the current deed in the registry.
Lot owners own to the centerline of the road, barring any stipulation in the deed, otherwise.
Easements do not relinquish ownership, only provide a legal right to pass and use. Do not confuse with "rangeways".
Additionally, maintenance of private roads require contributions by all. For example, if there are many lot owners sharing a private road (member of an HOA or not) all owners are legally required to share maintenance costs.
Private road
https://courts-state-nh-us.libguides...e%20...%22%20(
https://www.nh.gov/osi/resource-libr...quirements.pdf
https://alfanolawoffice.com/who-must...g%20the%20road.
MoBo town road list
https://www.moultonboroughnh.gov/sit..._road_list.pdf