I am about to begin a bathroom tiling project and I need help with the transition from the tile surface to the hallway-carpeted surface. See picture at:

www.shutterfly.com
email address-kaybjay2@hotmail.com
Password-hgtvpro (enter manually-no cut and paste-all lowercase)
Click on: “HGTVPRO” Album

My question is- should the underlayment and the tile butt up to the carpet line or should there be a gap to leave room for the transition strip? Or should the underlayment protrude past the tile surface to facilitate this? Also, what type of transition strip should I use. Thanks in advance.