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I assume that funds on that joint account do not belong to you - correct.
But when the owner will pass away - you become an owner of that account and all funds are treated as inherited.
For INCOME tax purposes inheritance is not taxable income in the US regardless the amount - as a recipient of inheritance you do not need to claim it as income.
There is no any amount limit.
Please see for reference IRS publication 525 -
Gifts and inheritances. In most cases, property you receive as a gift, bequest, or inheritance is not included in your income. However, if property you receive this way later produces income such as interest, dividends, or rents, that income is taxable to you....
So there is no income tax liability.
Federal estate taxes are paid by the estate - and only for large estates - with total value above $5,000,000. If your estate is below that threshold - there would not be any estate tax.