The Monkey and the Moon
This section will be unfortunately empty for now, but may be added to when I feel like doing more research on the matter. In my mind, this relationship is more one-sided on Renji's part, who has both admired and feared the 6th Division captain since his academy days. Byakuya also was the one who "took" Rukia, his childhood friend, from him, and to see him not treating her with the love and respect she deserved drove Renji up the wall.
In short, I feel that Byakuya affects Renji unequally, and since I'm most interested in relationships that represent the former's growth or personality, I can't quite put my finger on what to do about with these two just yet. Renji certainly grows, and his unbroken loyalty is a testament to Byakuya's charisma, but otherwise I don't have anything I can expand on yet in a more Byakuya perspective. To be continued!