Can anyone please tell me what is really the relationship between Kaito Kid and Shinichi or at least their parents.

Hello :)

In fact, Kid's father was the first Kid, he was also well known as a magician but anyone kwows that he was also the famous Kid except Shinichi's father, who was helping the police some time.

Shinichi's mother, who was still an actress, was given magic lectures by Kid's father.

When this last one disappeared, his son Kaito Kuroba discovered his double identity and decided to continue to be the Kid, in order to discover the reasons of his father's disappearance.

Kaito Kid's father is a magician who though shinichi's mother and vermouth(Sharon/Chris Veneyard)how to disguise...remember that yukiko and sharon vineyard were both actres...