Assuming share of the parental home after divorce

Hello everyone, I need some advice on a matter.

The following situation: My parents bought a house together and are both listed in the land register.
In the meantime, they have divorced and my mother no longer lives there. I have agreed with her that I will buy her share of the house from her. The house is being converted into three apartments and I will get one of them.
So far, the plan was to first push through the building application with the subdivision plan and then go to the notary with it.
I am wondering whether I could simply buy the "right to her share of the house" beforehand and also have it registered with the notary?

Another question that comes up:
They were in a community of accrued gains. No assets were brought into the marriage (as none existed). During the divorce, they completely left the house issue out since neither of them had any idea how to proceed with it. My mother was only occasionally employed during the marriage and the loan was completely paid by my father during the marriage. Can I assume that my mother's ownership share amounts to 50% of the total property?
If any information is missing, I will gladly provide it.
Best regards, Daniel

Hello Daniel,
make an appointment for a consultation with the notary. Although he will not advise you personally, his specialized employees will (in Bavaria they are called Notarinspektoren). And if the subsequent notarization takes place with this notary, there will be no or only minimal additional costs. The job of the notary, or rather his office, is not only to notarize but also to provide neutral advice between the parties.
If your parents indeed had no assets before the marriage and none were brought in later through inheritance or gifts, you can assume that your mother's share of the house is 50%.
However, I cannot imagine that the house was "left out" during the divorce, as all assets must be recorded. It may of course be that no negotiations took place regarding the house, which would also speak in favor of a 50/50 division.

The following situation: My parents bought a house together and both are also listed in the land register.

My mother was only temporarily employed during the marriage and the loan was completely paid by my father during the marriage. Can I assume that my mother's ownership share is 50% of the total ownership?

If they are each listed as 1/2 in the land register, then you can assume that. It does not matter who paid the loan.