As some have mentioned, the real answer is whatever works, as every relationship is different.

With that out of the way however I would generally reccomend three different alternatives, which will depend on what the goal/long term plan is.

1. Equal ownership of the appartment Your GF will either buy in with half of the sum already paid down or "take over" the remainder of thr mortgage that would equal owning half the appartment once paid down, and cover the corresponding portion of monthly down payments. Depending on their current savings this may or may not be feasible. If not able to pay upfront, it may be possible to calculate how much would be needed to eventuallly get to equal ownership and try to save up and pay bit by bit. Running expenses split 50/50

2. Partial ownership of the appartment Either split the mortgage equally or however large a portion you GF is able to cover financially, and at the point of either movibg out or selling calculate the what share of ownership those dowbpayments have equated. Depending on how long you intend to live their before selling or how willing you both are to commit at the current stage of relationship, this might be the best/fairest way to start of. Can easily transition into option 1 down the line. Running expenses split 50/50

3. No ownership share of the apparment. You keep paying all mortgage fees and you just split all other running expenses 50/50. If you at some point sell the appartment to buy a new one/a house together you could solve the potential inequality in funds by you coverkng the bigger part of the upfront cost, while she covers a bigger part of the resulting mortgage so that it eventually equates to a 50/50 ownership.

Hope this helps :)