After I made that post I found that the WEL Energy Trust is to be wound up by 2073, so I guess ultimately the lines company will be sold as well

"As per the Trust Deed, on winding up of the Trust in 2073, the fund will be distributed to Territorial Authorities (Capital Beneficiaries) in specific proportions (Hamilton City Council – 63%, Waikato District Council – 35%, Waipa District Council – 2%)."