The Bekenstein bound? A maximum number of bits can be placed on the surface of sphere. Beyond that it turns into a black hole.

Mind you, one or two other practical limits might come into play before a memory chip hits that one. :-)

[1] https://en.wikipedia.org/wiki/Bekenstein_bound

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Edit:

The maximum information capacity of a radio antenna is limited by the surface area enclosing the antenna. One could theorise that that in addition to a maximum density of information storage there will also be a limit on the error free rate at which information can be sent to/from a storage system system, probably related to the surface area enclosing the system.