Source: i use it
Ubiquiti has a feature called Zero-Handoff [1] which indeed requires the controller's participation. The APs all end up on the same RF channel in this arrangement. While I've not used this feature, multiple APs on the same channel tends to be a bad idea and I much prefer my setup of simply using the same SSID on multiple APs/channels.
[1]: https://help.ubnt.com/hc/en-us/articles/205144590-UniFi-What...
Meraki insists you need to disable the wireless on the security gateway and ONLY use a "combined network" of APs to have the same SSID for roaming.
Granted, I know very little about how it actually works -- I think they use separate channels, unlike what folks here discuss for Ubiquiti.
note that unifi does not mention requiring controller running (and i do not have mine running ever and it works)