If the person has not died testate - inheritance by intestacy shall be applied.
The first heirs are the children and the spouse of the deceased, which inherit equal portions. If some child does not inherit, the hereditary portion goes in equal portion to that child's offspring. Should those children not inherit, so it will be their offspring. In cases when the marriage lasted until the death of the spouse, the marital community property will be settled first and only the remaining half will be inherited by the surviving spouse and the children.
If the deceased had no offspring, the heirs in the second group are the spouse and parents of the testator and those, who lived with the deceased in a common household for at least one year before his/her death. The heirs in the third group are the testator's siblings and persons again, who lived with the deceased in a common household for at least one year before his/her death.
Should any of the testator's siblings not inherit, the sibling's hereditary portion goes in equal portions to his/her children. In the fourth group, the heirs to equal portions are the grand parents of the testator and if none of them inherits, their children shall inherit equal portions.
If you are not in official wedlock, the best way is to draw up a testament at a notary. In this way you avoid problems with the succession proceeding. The testament must be drawn up by each of the partners separately.
Inheritance of debts
You should also bear in mind that up to the amount of the acquired succession, the heir is also responsible for adequate costs pertaining to the testator's funeral as well as his/her debts, which got devolved to him along with the succession. If there are several heirs, they have to share those costs in the proportion of the acquired property. If the succession is over-indebted, i.e. the debts actually exceed the value of the property, to the heirs may agree with the creditors that they will cede the succession to them to pay the debts. Such an agreement however, needs to be approved by the court.