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In the news, Heiji has been publicly declared the "Great Detective of the West", while Shinichi Kudo is the "Great Detective of the East". As a result, Heiji showed up unannounced at the Mouri Detective Agency looking for Kudo, seeking to challenge his rival to a showdown of wits. (In fact, they had such a contest before, three years previously, during a skiing trip in the Yamagata prefecture, although they never learned about each other's identities at that time.) Heiji was soundly defeated in the following case after Conan Edogawa temporarily turned back into Shinichi, but he gained a lot of respect for Shinichi in the process.

During their second encounter, Conan knocked Heiji out to use him as the mouthpiece for the voice-changing bow-tie. But during his final presentation of the facts, Heiji awoke prematurely and discovered Conan's secret, and in the end managed to blackmail Conan into revealing all. Ever since that revelation, Heiji has been helping Conan in hiding his secret identity, though he constantly slips up by calling him "Kudo" in front of Ran and Kazuha.

Heiji and Conan most often congenially team up to solve assorted cases. Heiji has also helped Conan investigate the Black Organization on several occasions, such as when the two investigated Jodie Starling, or when Heiji investigated Eisuke Hondou on his own and then told Conan his findings, but he never had a real direct confrontation with the primary antagonist.

He has also helped cover for Conan during several of the brief instances where Conan regained his true adolescent age, and has even disguised himself as Shinichi on several occasions in order to protect his identity, even though he is not very good at it (mostly owing to his distinctive Kansai dialect). When not working on a case, he regularly attempts to invite Conan to take in the sights and culinary delights of Osaka, which he considers more wholesome than Tokyo's.

(Source: Detective Conan World)

Detective Conan: The Culprit Hanzawa