I have noticed that at pretty much every Chabad shul I have ever attended, the same tunes were always used for certain parts of davening on Shabbos. For example, they all use the same tune for ha-aderet v'ha-emunah during psukei d'zimra as well as for the line in the kedusha for musaf that begins hu Elokeinu, hu avinu. They also all use the same tune for ata bechartanu during yamim tovim. Every Chabad shul also seems to sing al tira... at the end of davening, although I have noticed variations in the tune used.
Is there a reason why almost every Chabad shul seems to use these tunes for these parts of davening? What is the origin of the tunes? Were they favorite niggunim of one of the rebbes? How long have Chabad shuls used these uniform tunes?