I was in a study hall [beit midrash] today and someone asked a question about a woman who became a convert while pregnant. The question was if her daughter can marry a [cohen] priest.  I have no idea why he asked me this question, but it just so happened  that the previous day I was looking at a book containing questions and answers of Rav Elyashiv that happened to have that very question.    It was about a woman that had converted and was pregnant and had lost her documents and then came to Israel and had to convert again. It was clear from the answer of Rav Elyashiv that that daughter is allowed to marry a Cohen [since she was born by a regular Jewish woman].But in another place I noticed Rav Elyashiv bring up this issue in terms of a question if a fetus is part of the mother. Does this depend on that question?     

The issue here is that there are a few types of women that a priest can not marry, e.g. a convert, a woman who has had relations with someone forbidden to her [zona], or a woman who has had relations with someone forbidden to the priesthood, or a divorced woman.