Demi Moore to Ashton Kutcher -- What's Mine Is Mine; What's Yours is Mine!

Demi Moore has been like a heat-seeking missile ... squarely aimed at the bank of Ashton Kutcher ... sources connected with the couple tell TMZ.

Our sources say Demi -- who ironically is richer than Ashton -- has demanded spousal support from Ashton. It's particularly surprising because we're told Demi recently got around $15 million belatedly from ex-hubby Bruce Willis in connection with their divorce. If the case doesn't settle it's virtually certain a judge would reject Demi's spousal support claim.

Sources say Demi wants Ashton to help pay for the renovations to her New York apartment ... something he's unwilling to do. BTW ... we're told the apartment (in the ritzy San Remo building) is worth somewhere between $25 mil and $40 mil!

There are other sticking points. We're told Demi is upset because Ashton got involved in an online business and she feels entitled to part of it. Problem is ... he got involved AFTER they split, so it's almost certainly his separate property.

Our sources say Ashton is willing to give Demi something to end the battle ... the question is how much? Demi scored big in her divorce from Bruce Willis -- getting a reported $90 million. Her net worth is estimated at $150 million. Ashton's reportedly $10 million behind her.

In the end, our sources say Demi is backing off a bunch of her demands and the case could settle as early as next month.