Well they been roaming around for thousands of year ...they were also the sages pets sooo.Title?
This.Based on this yes.
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But, only to a certain level of physical growth beyond which there appearance won't change much imo.
Revive Kaguya or restoring the chakra fruit could potentially destroy them imo.Baby Kurama is so cute, yes they grow.
They are said to be immortal but I doubt it, Madara was also said to be immortal...