I named my grandchild as the joint owner of my brokerage account. What will her tax basis in the account be when I die (she didn’t contribute anything)?

In the case of a joint tenancy with someone who is not a spouse and who did not contribute anything, the basis depends on the estate tax value of the property (even if the estate is too small to be required to file an estate tax return). This is usually the value of the account on the date of death. An alternate valuation date of six months later can be used only if the estate files a return and elects this valuation date (which is done if the overall value of assets in the estate declines).