Home state

In my papers from the court it states: ‘That North Carolina remains the home state of the aforesaid minor
children born of the marriage and this court has jurisdication pursuant to the provisions of North Carolina
General Statues 50-A- 201 and 50 A-203’ The children have not lived in NC for 6 years. Could you explain
this to me please.

North Carolina will remain the home state of the children, unless and until all parties no longer live there (including the other parent).

Does this mean that NC should be responsible for them such as health care since the
children do not have insurance?
Also can I request for a change of venue? My divorce issues have been going on
since 2003 and I would really like to get it all over with.

No, it means that NC has jurisdiction over the custody issues.
You may attempt to have NC release jurisdiction of the case based on the fact that the children have lived elsewhere for so long.