Yea, I know I have too much time on my hands but... I have 2 players that are 1st ballot HOFers in one world. Both are mid to late 30's age wise and will not be offered contracts for the upcoming season. Both have been with my franchise for the largest part of their careers and one has spent his entire career with the franchise albeit with several owners and team name changes. My question is, if I let these guys walk and another owner picks them up for next season, when they do go to the HOF will they wear my teams cap or the cap of the last team they played?

Definitely not the last team - pretty sure it's simply where they spent the most time.

And also players show up with the cap of where the franchise is currently located rather than where it might have been when they played there...

its done by games played at the ML level. if you are on top of that list hes gonna have your Cap!