Yevamot, Chapter Eleven, Mishnah Two
This mishnah refers to a converts participation in halitzah and yibbum.
1) The sons of a female convert who converted with her do not perform halitzah or yibbum, even if the one was not conceived in holiness but was born in holiness, and the other was both conceived and born in holiness.
2) So also [is the law] where the sons of a female slave were freed together with her.
Section one: When a person crosses the boundary and converts into Judaism, he legally loses his genealogical ties to his former family. Therefore, when a woman converts with her sons, her sons lose their ties to their father and are no longer legally considered to be paternal brothers. Since only paternal brothers perform yibbum or halitzah, these brothers do not. Should the wife of one of them die, the other brothers do not perform halitzah and yibbum for her. The widow is exempt as if her husband did not have any paternal brothers.
This law is true even if one of the brothers was conceived before the mother converted (not in holiness, see Deuteronomy 23:1) and born after she converted (in holiness) and the other brother conceived and born after she converted. Since at the time of the conception of the first brother the mother was not Jewish, the ties to his father do not carry over. Only if both brothers were both conceived and born after the mother had converted are they considered paternal brothers (assuming they have the same father).
Section two: The same exact rules apply with regard to the freeing of a female slave. When a female slave is freed she becomes fully Jewish, and therefore the emancipation of slaves is somewhat like conversion.