ties broken made anew?

The apportation of male and female is the same. All of us have one set of chromosomes from our father and one from our mother (though they may have recombined in the meiosis process, so grandparents could be more or less represented but on random basis).

The only diference in the genetic aspect comes from the so-called haploid genealogies, that can only trace purely male-male or female-female lineages and not those that have changed gender at some point (all but two, the farther back you go the more ancestors that aren't represented in such genetic genealogies). For instance, if my genome would analized by such partial methods, I would probably come out to be 100% Basque but in fact I have much foreign blood, just that my purely maternal and purely paternal lineages happen to be local as far as I can trace them.

What you say can be only understood from a Patriarchal viewpoint. As it is obvious that biologically females reproduce one's lineage as well as males. The problem is that in most societies they don't carry the surname on to the grandchildren but that's purely conventional, not biological.