If I understand you correctly your companion put your name on two checking accounts, died, his probate estate that is not closed and in the meantime dividends from his investments have been deposited into the accounts, so who owns the dividends (and interest on them). Technically this was wrong to do with one possible exception, because unless you were co-owners of the investments and entitled to inherit them on his death, the dividends belonged to his estate, and should have gone into an executor's or administrator's separate account. So the exception is where you are entitled to inherit his portion of the investment. If not, the problem now is properly accounting for the dividends and any interest that has accrued on them. You really need to have an attorney involved, and at the bare minimum if this is an open probate case you should ask the judge for direction through proper motion practice.
