Ejerlejlighed = You’re the sole owner of the apartment and any and all debts associated with that apartment alone.
Andelslejlighed = You’re the owner of the rights to live in the apartment (Communal debt, what you refer to as shareholder complexes)

You should be very carefull when buying a shareholder complex here in Denmark. Some of them don’t have a very good economy and the expense of living in one can be extremely high compared to for example a rented apartment. They can also end up declaring bankcruptcy. You should have an accountant look through it for any and all dangerous loan types and if they’re actually paying off the debts. (the value of the apartment(s) goes up over the years (andelskronen = the value of the share).

Also, negotiate the price hard. The real estate property here in Denmark has gone down in estimated value, but sellers haven’t always realized that. You can usually cut off 5-10% from the price. Sometimes more. You also pay real estate tax each year, which is 1% of the ‘official value’ that’s not what you paid, but what the government estimates it to be worth. The real estate broker.. isn’t a broker either, he’s the sellers man. He’s not on your side and just a salesman.