Members of Congress and the New York State attorney general demanded detailed information Thursday on how tens of billions of taxpayer dollars flowed through the American International Group during its crisis last fall and ended up in the coffers of several dozen big banks, shielding them from losses. The new inquiries shine a spotlight on a question that is exponentially bigger, in dollars, than the $165 million in bonuses that A.I.G. paid out this month, but which has been overshadowed until now by the uproar over the bonuses. We would like to know if the A.I.G. counterparty payments, as made, were in the best interests of the taxpayers who provided the funding," said Representative Elijah E. Cummings, Democrat of Maryland, in a letter to Neil M. Barofsky, the special inspector general for the Troubled Asset Relief Program. The banks and investment firms that ended up with A.I.G.'s bailout money last fall were, in many cases, counterparties to derivatives contracts it had sold, known as credit-default swaps, which guaranteed the value of assets in their investment portfolios. They included Wall Street firms, like Goldman Sachs, JPMorgan Chase and Merrill Lynch, that have successfully resisted efforts to regulate credit derivatives in the past. In several hearings this month, members of Congress said they believed the derivatives had often been used to speculate, not to manage risk. They have expressed outrage that A.I.G.'s trading partners got 100 cents on the dollar for their money-losing trades when ordinary Americans paying for the bailout have suffered big losses in their 401(k) accounts and other investments.