Well if the Potters are related to Godric Gryffindor than it would be through James side of the family since Lily was muggle born. This is possible because JKR has said that in Deathly Hallows we will learn more about James family, and why the Potters were so weathy. If we belive that this theory is true than all Harrys money could be leftover from Godric Gryffindor's inheritance.

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