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If you are referring to dividends and capital gain distributions that were reinvested in the same mutual fund or stock then, yes, those amounts add to the cost basis.
For any capital gains from the sale of shares the long tern gain that was included in income is not part of the cost basis. But, you may have bought additional shares with the proceeds from the sale that, of course, would be a cost of those new shares.
I hope this helps.
The fact that it is a UGMA account does not change the basic application of the rules for cost basis. Think of this like you would your own brokerage account.
When you sell stocks or funds and report capital gains and pay income taxes the taxes paid are not part of an increase in basis. The fact that you leave the proceeds in your brokerage account will only have an effect on basis to the extent that you reinvest those funds. The reinvested funds may later have more gains that are taxed; but the amount that has already been taxed is not taxed again as the amount that was invested is the cost basis for the later sales. The same will be true for the UGMA account.
I can make gains over and over using the same money investing in one stock or fund later selling and paying tax on the gain and reinvesting in another stock or fund later selling and paying tax on the second gain and so on; but the funds that I have paid tax on are not taxed again in the later sales. Neither in a regular brokerage or in the UGMA account do you have to pay tax twice. Tax is only due on the gains not on any purchases.
When you got your distribution there will be a cost basis for the investments held in the account and not sold at some earlier date. This information is either provided by the broker or can be computed from all of the purchase details for initial purchases and later reinvested amounts.
I hope this helps to clarify for you.
Did you get Form 2349 that reported capital gain distributions that you did include in income and that were not distributed by the mutual fund company to his account? That is not very common. In most cases it is reversed the following year (the gains are distributed or an adjustment is made in the distrbutions for the prior year undistributed amount).
It seems you may be confusing capital gain distributions which you did get from the mutual fund, reported to you on 1099-DIV on which you pay tax and those that are being discussed in that part of the publication (undistributed capital gain on Form 2349) which are not (yet) paid out by the mutual fund company.
Or you may still be thinking that there is a difference in tax treatment between amounts that are not obtainable from the UGMA account (due to the age of the owner) and those in a regular broker account. There is no difference.
You did pay tax on an amount that was not permitted to be given to the minor in the year 2000; but that has nothing to do with amounts that were not distributed by the mutual fund company (undistributed capital gain) to his account.