To fill the friendship meter, you must bring it corpses. The amount of friendship gained from a corpse is dependant on the corpses drag weight. For example, a managarmr with 250 drag weight will fill up the friendship meter by half, where as a yutyrannus with 500 drag weight will fully fill up the meter. (Note that this works with baby creatures) Iโ€™m fairly certain that the actual taming of the carch (killing creatures) is based on their health. So the more health a creature has, the more taming affinity it will reward. Hope this helps :)

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