What's interesting is that the line of succession from the 14th century to the present day is so well documented on the wiki page below
en.wikipedia.org/wiki/Parakala_…
Perhaps it awaits a historian to study the primary sources closely, separate legend from fact, and construct an academic history for these ancient, yet living, institutions of India!
Succession at the top is a problem in many of these mathas. Finding talented, willing, and virtuous monks can be hard (and that's a hard combination)
Even within Sri-Vaishnavism, you have other mutts of comparable antiquity -
The Ahobila Mutt - about 6 centuries old
Andavan Ashramam - about 3 centuries old
And these are very much living institutions
The three mathas that I mentioned chiefly concern the Vadakalai population of the Iyengar community - whose population in India is most likely less than a million
But how long will this last?
Already the strong endogamy holding the community together has loosened significantly
These changes are imperceptible - they have happened in the past 20-30 years
And the communities, in my view, are not coming to terms with these changes...
Otherwise, the state of affairs won't last in a set up where endogamy is loosening by the day, and you don't have a "captive audience" like you did evne 50 yrs ago
The sense of security and cocksure complacency often found in these institutions is merely the lull before the impending storm