If you fly A320 you cannot go to B737 or A380 unless you complete TR. Basically it takes a month to transfer with about 30h simulator hours plus 4 or 6 real landings
Not entirely true. If you fly one (modern) Airbus you can do a CCQ to fly another type of Airbus. It's roughly about one quarter to one half the time of a full type rating. From Airbus themselves, the A320 to A330/A340 = 1 week. A320 to A380 = 15 days.
And Airbus are working on a common type rating for A330 and A350, so that if you have an A330 endorsement, you don't need and full flight simulator sessions to fly the A350.