@Him - Transitioning to a new work center is pretty similar to what you experience during cross-training except you are now permanently listed under the new work center and will spend the majority of your time there. It is also similar to when you start a new job.
I can share my own experience with you!
I used to work softlines at another retailer but then moved over to HR at Target. I needed to learn Target in general plus a load of HR policies and procedures while having to simultaneously cross-train in 2 other areas of the store. It was stressful since I was a newbie and there was so much to pick up on (my coworker, also new, quit after a month).
Anyway, I conquered the transition obstacles by proactively seeking information, multi-tasking, and communicating often. Whatever I encounter that wasn't taught to me during training week, I sought out the details, myself, by asking an experienced person about it or looking it up on the computer. Whenever a whole bunch of people needed me to do things, I wrote stuff down, prioritized the tasks within my workload, tackled each of them, and kept everyone up-to-date on the statuses. My goal was that no one should be ever be left wondering what happened with what they asked me to do. I always followed up with everyone. Most importantly, I made sure my own ETL knew my efforts so it reflected in their review of my performance. After all, my own leader was the one who decided whether or not to keep me so this was vital.