Do most BB analysts leave after their 2nd year or 3rd year?

A lot of questions there but I'll answer a few of them:

• The BB is trending towards 2 year analysts programs as many have removed the third year analyst year - opting for promotion after 2 years
• A number of banks want to retain analysts now adays so they are trying to keep analysts when possible - so if you want to stay and you're decent they will likely find a spot for you
• If the bank does have a 3rd year analyst program it doesn't really matter when you leave. If you strike out in on-cycle recruiting during your frist year or if you decide late that you want to recruit, and you have your heart set on a MF or UMM you can take a second run at it in on-cycle 2 - with a plan to start in 2 years (so after your third year as an analyst). Going into the second on-cycle window you will have an edge over your first year peers since you will likely be a better modeler and will have real deal experience - so that can be helpful.
  - Interestingly, some people will do on-cycle their second year - take the A to A promotion with the intention of starting at their buy side exit op after their 1st year as an associate - this may burn some bridges at your bank, but an option

Just observations based on my experiences. Hope this helps.