Finland would probably receive all of Soviet Karelia and perhaps all of the Kola Penninsula and surrounding land.
Finland
wanted essentially what it had occupied by 1942 IOTL plus Kola. There was an official study written about this during the Continuation War, basing the claim on the extent of "ancestral Finnic homelands". The ensuing "Three Istmus Line" was considered as most defensible (and this very idea betrays how Finnish leaders thought about the chances of destroying the USSR/Russia as an entity). Kola, even if not entirely ur-historically Finnic, holds huge mineral resources. And that is why Hitler was unsure about wanting to give it to the Finns.
Personally I believe in the end the Nazis would have allowed Finns to administer the peninsula, in exchange for mining rights. There is nothing beyond the metals and minerals in the area that the Reich doesn't already have/get from somewhere else.
It is also possible the Nazis would want to hoist additional administrative/occupational duties to the Finns, extending the areas attached (permanently or temporarily) to this "Greater Finland"
beyond what Helsinki demands. The Reich will have its hands full in trying to keep order in what it has gobbled up and manpower is becoming short by the time the wildernesses of northwestern Russia are being considered.