@ehBeth,
a) there must be a father registered,
b) he has to pay according to a list called the "Düsseldorfer Tabelle" (that's a tablet by the regionl court in Düsseldof, used as a basis by all courts all over Germany).
I think that it's slightly here as it is in Canada.
This "a father has to pay" is regulated in various laws ("spousal support" it would be in the USA, "maintenance" in England).
If a mother doesn't want it ...
nullo actore nullus iudex, no plaintiff, no judge.
As far as I know, in most districts of Berlin (like elsewhere in Germany), the local
Jugendamt ("youth welfare office") will at least have a look at the situation of a single mother's child, especially, if there's no registered father.