Yevamot 47 - Accepting converts
A man came to Rav Yehudah and said, "Even though everybody considers me Jewish, but the truth is that I have converted myself, without the presence of a court of three." Rav Yehudah asked, "Do you have children?" The man answered "yes." Rabbi Yehudah then said, "You are believed to disqualify yourself from being Jewish, but not to disqualify your children."
Why is the man believed about himself? - Because anybody can create a prohibition with his own words, in the situation where he stands to lose. But why is he not believed about his children? After all, a father is believed to tell us which one of this sons is the firstborn!? - Because once we believe him that he is an idolater, then he is no longer qualified to testify on Jewish matters. Others say that the man is believe even about his children, precisly because we would believe him about the firstborn, but he is not believed about his grandchildren.
In general, if one comes and says that he wishes to convert and become Jewish, they tell him that he is joining a persecuted and pursued people, and if he still persists, they begin the process right away. They also tell him about a few of the mitzvot that he will have to keep, and inform of the seriousness of the prohibitions of Shabbat and the like. However, they also tell him about reward in the World to Come. Finally, they inform him that he will have to give charity, and in Israel of the tithes that he will have to give. However, they don't overwhelm him with stringencies, as is learned from the behavior of Naomi toward Ruth, a righteous convert.
Art: Children by Boris Dmitrievich Grigoriev