Prince's Heirs Worried Estate's Burning Cash Will Leave Them With Nothing

Prince's estate is spending a ton of cash -- at times more than $600k PER MONTH -- and dropping that kinda loot has the singer's heirs worried they'll be left with nothing when it's their turn to collect.

Sources close to Prince's heirs tell TMZ ... they're dumbfounded at how much money it costs to manage the late singer's estate. We're told at the current burn rate, heirs feel there's gonna be close to nothing when it's time to distribute the inheritance.

According to docs -- obtained by TMZ -- Comerica's monthly fee to manage the estate is $125k per month. Comerica also hired the law firm Fredrikson & Byron P.A. to rep the estate in court (i.e. Prince's label suing Roc Nation), supervise and coordinate with accountants and advise on tax-related issues. Last November alone, the law firm billed more than $440k in fees and expenses.

The spending keeps going ... F&B then hired other attorneys to deal with trademarks, oversea litigation and services on deal proposals, among other things.

Comerica, for its part, has painstakingly broken down in more than 600 pages of invoices exactly where the money's going and why it costs so much to manage the estate, which is reportedly worth around $250 mil.