Ultima 1 is made of five different executables, each responsible for different parts of the game. When the game must pass from one executable to the next, the current executable saves your character in a temporary savegame file called INUSE.U1. The next executable then loads this character so that you can seamlessly continue your game.
Everything starts with ULTIMA.EXE, which initialises the graphics mode and starts the game. An interesting thing to note is that the game never closes the graphics mode. Ultimas 1 to 4 did not allow you to quit the game, so once you started playing, you would have to reboot to go back to DOS.
You can choose which graphics mode to use by passing it as a parameter, e.g. ultima cga starts the game in CGA mode. This apparently works for Ultimas 1 to 5. [Thanks to Natreg for this one]