How autonomous were different princely states in British India?

by therandshow

I get the sense that level of autonomy varied, but I am curious if this was a formal difference based on prestige (like gun salute status) or treaties, an informal difference based on area and population, or if this was in large part determined by the personality of the ruler and their ability to navigate the politics of British India.

voyeur324

/u/drylaw has previously discussed the autonomy of the princely states in response to Why was Kashmir not partitioned along with the rest of India?