As I understand the Shul is generally owned by the Shliach (he sets up a (or uses an existing) non-profit for the legal aspects, but it's almost completely in his hands). This is done for several reasons:
- AFAIK, most shuls generally exists by virtue of the community. Baalei Battim who live in a certain neighborhood make a shul, then they look for a Rabbi who fits their needs. Chabad rabbis look for the community. They make their own shul and then look for Baalei Battim. Therefore, the governance is more in line with a Shtiebel than a classical Shul.
- A Chabad shliach's purpose is to deal with people that are much less religious than him. If he let them vote or make boards, the Balei Battim may just turn around and turn it into a ... (A normal shul also has this problem, but they have no choice. The Rabbi was brought down by them. A Chabad Shliach is technically capable of being independent from the Baalei Battim).
There are no hard and fast rules. 770 has elections for Gabbaoyim (and Crown Heights in general has elections for Rabbonim). Some Shuls (in Crown Heights) have boards. In some, the old Rov bequeathed the position to a new one.