Star Stamps are objects collected in the Story Mode of Mario Party 3. When the Millennium Star fell from space, Mario and his friends argued over who had the right to claim it and be named the Superstar. A Lakitu suggested that they should have a contest to settle this problem. The Millennium Star came to life at that moment and said that whoever obtains all seven Star Stamps--each named for a different quality--shall be his rightful owner. The characters were to compete for each Stamp on a Battle Royale map related to the Stamp's trait. If the player wins, the Millennium Star begins to award the Stamp but is interrupted by a character who did not compete in the Battle Royale. This character claims to be a more rightful owner of the Stamp thanks to a greater claim to the quality it represents. This conflict is settled by a duel between the player and this new opponent on a Duel Map.
After the first five Stamps have been collected, this pattern is broken. Daisy enters too soon, interrupting the Millennium Star and claiming to be the rightful owner of the Beauty Star before the Battle Royale has even taken place. The Millennium Star comes close to falling for her beauty and awarding her the Stamp without contest, before ultimately letting the player duel her without entering a Battle Royale first.
Waluigi steals the Mischief Star and challenges the player to a fight on the Waluigi's Island Battle Royale map. Since he takes part in the Battle Royale, there is no duel for this final Stamp. Bowser also tries to lay claim to the Star Stamps but is completely unsuccessful, often arriving after the Stamp has been awarded.
The Battle Royale map used to earn a Stamp, the character who will challenge the player over it and the Duel map used to settle the challenge are listed in the chart below. If the player chooses a character other than Luigi, he fills that character's vacated spot but the location of the duel remains the same. Neither Daisy nor Waluigi can be chosen by the player, as they fill unique roles.
List of Star Stamps
Note that Luigi replaces the character that the player picked, so he doesn't have his own Star Stamp or Duel Map, claiming those otherwise used by the chosen character. Since Daisy and Waluigi cannot be chosen for story mode, Luigi will never challenge the player for the Beauty or Mischief Star Stamp.
In other word: For each Stamp If Luigi is chosen, then the default characters will battle him. Otherwise Luigi will replace the character that the player chose.