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After reading the latest chapter I think that Law came to the island upon hearing the distress call with Luffy on it. He may have already been in the area or was some how notified by Jinbe about the Strawhats arriving in the New World and he was looking to meet up with Luffy, be it to fight or to be civilized like Shanks and Mihawk. I think the characters that have been combined so far with animals is just a "coincidence" to Law being there but he almost absolutely is the one who chopped up the head. I think after trying to get rid of the marines quick he will chase after the SH to find out where Luffy is.