Why your home ends up with the notary
As long as you are co-owners, your home is not automatically divided after a divorce. Your name and your ex-partner's name remain on the purchase deed, and that situation legally continues until someone takes action. This is called undivided co-ownership: you both own a share, but neither can decide alone about the whole.
To properly end this undivided co-ownership, you will eventually need the notary. The notary is the only one who can draw up the official deed that transfers ownership, either to one of you or to a buyer. Without that deed, nothing changes regarding who is the legal owner, even if you have been apart for a long time.
The notary works neutrally. He or she does not take sides but ensures everything is legally correct and that the proceeds are divided fairly.

