Thank you for reaching out to us with your question. The situation you are describing is regulated in “The Cohabitees Act” (sambolagen, SL).

A property division/bodelning 

When a couple separates, the opportunity to apply for a property division arises (called a bodelning in Swedish). This can be done within a year of the separation (8 § st 2 SL). If the couple is having trouble cooperating, one can also apply for an estate distribution executor (bodelningsförrättare). 

A home bought for the purpose of living together is considered “samboegendom” no matter who bought it or who is listed as the owner. That means that it is included in the property division. Regarding which person gets to keep on living in the home: that depends on who has the greatest need for it (16 § 2 st SL). This is decided through an assessment of all the different circumstances. For example if there are children who will be living with one of the parents, that parent usually gets to keep on living in the home. 

Recommendation 

To answer your question, it does not matter that your ex-partner is the one that paid all the deposits, you both have equal rights to the apartment. If you are fine with him living there, then he will have to buy you out by giving you your share of the apartment in money. If both of you want to keep on living in the apartment, then the one who needs it the most will get to continue living there.  

I hope this answer has provided some insight!