South Africans woke up Sunday to find new details about the death of Oscar Pistorius' girlfriend splashed all over the country's newspapers.

The tidbits reported by City Press are said to come from anonymous police sources.

The paper says a bloody cricket bat found at Pistorius' home could become a key piece of evidence in the case.  Steenkamp's skull is said to have been found "crushed".  Police are considering that Steenkamp may have been beaten with the bat, but also that she may have used it to defend herself from her attacker.

City Press also reports that Steenkamp was first shot in the bedroom of the Olympian's home & may have been running to hide in the bathroom when she was hit 3 more times.

Police haven't commented on these new details.

Steenkamp will be cremated & remembered at a private funeral in her hometown of Port Elizabeth South Africa on Tuesday.

Pistorius told family members he'd mistaken Steenkamp for an intruder.  A police source tells City Press she was found dead in her nightie, her overnight bag in the bedroom & that "it was clear that both of them had slept in the bed".

Speaking for Pistorius' family, uncle Arnold Pistorius said: “We have no doubt there is no substance to the allegation and that the state’s own case, including its own forensic evidence, strongly refutes any possibility of a premeditated murder.”