The lineage's seat is Mount Longhu in Jiangxi, where the descendants of Zhang Daoling held the title of Celestial Master and, from the Tang onward, imperial recognition. The office is hereditary, which is unusual in Chinese religion, and has made its succession a matter of record rather than of election.
That record broke in 1949. The sixty-third Celestial Master, Zhang Enpu, left the mainland for Taiwan, carrying the lineage with him, and died there in 1969. His successor held the title until his death in 2008, and since then the succession has been open. Several claimants to the sixty-fifth office have asserted themselves in mainland China and others in Taiwan, and no authority exists that could adjudicate between them, which is the difficulty with a hereditary office whose family has been split by a border and whose principal seat lies in a state that administers religion through a body of its own.
Organised Taoism in the People's Republic accordingly runs through the state-supervised association rather than through any Celestial Master. Zhengyi ordination continues within that structure, and Mount Longhu functions.
The dispute matters less to ordinary practice than the structure might suggest. A Zhengyi priest's standing rests on his register, his manuscripts and his community's acceptance, and a village engaging him for a jiao is not consulting a central roll of authority. The office is a symbol of continuity, and the argument over it is an argument about the symbol.