http://www.tblc.org/reciprocal/patron_libraries.php
This probably varies from library to library though as it looks like each library can decide what to do for each potential reciprocal borrower.
What happened with my account disappearing from Oldsmar is my three years of registration at that library came to an end. Three years passes quickly when you are in TV.
Funny that Hillsborough Library System (Tampa's) seems to have pulled out of the Reciprocal Borrowing contract.