On the level of biology some of the variants are
1) Is the egg fertilized in the donor or outside?
2) If outside - is it in the host mother or in vitro?
3) At what stage of development is the transfer to the host mother done?.
4) If the birth mother received an ovarian transplant - do the eggs belong to her or the donor?
5) If the recipient of an ovarian transplant is not the owner of the egss - is her husband allowed to have relations with her - i.e., is this adultery?
6) Does it matter who the father is?
7) What if genetic material is taken from another person's skin cells or perhaps from a combination of donors - is there any impact on identity?
8) What if the donor is not Jewish or the surrogate is not Jewish - does that impact identity?
9) what if the surrogate mother is an animal or an incubator - or even the father?
10) There are kabbalistic sources which state that Jewish identity and yichus is dependent on producing a child through sexual relations - so a child produced by in vitro ferilization is significantly different.
11) What if the host mother was converted at some time during gestation - what impact does this have on the Jewish identity of the child?
As far as I have been able to ascertain there is only a single source which deals directly with this issue - these are the medrashim that say that Dinah was transferred from the womb of Rachel to Leah and Yosef from Leah to Rachel. These medrashim clearly hold that identity is determined solely by the birth mother. But learning halacha from medrashim is problematic
These issues also impact on the issue of conversion. R' Bleich cites the view of Rav Sternbuch in who uses the events of Sinai to help resolve some of these issues.