The division of mortgage-related assets can affect each spouse's ability to qualify for a new mortgage in several ways:

1. **Credit and debt-to-income ratio**: The division of mortgage-related debts and assets can impact each spouse's credit score and debt-to-income ratio, which are important factors lenders consider when approving a mortgage application.

2. **Ownership of assets**: If one spouse retains ownership of the marital home and the associated mortgage debt, it could impact their ability to qualify for a new mortgage, as the existing debt would be factored into their financial profile.

3. **Equity position**: The division of equity from the sale of the marital home or other properties can affect each spouse's ability to make a down payment on a new mortgage. More equity could improve their chances of qualifying for a mortgage with favorable terms.

4. **Alimony and child support**: If one spouse is receiving alimony or child support payments as part of the divorce settlement, it could be considered as income when applying for a new mortgage, potentially improving their ability to qualify.

Overall, each spouse's individual financial situation, including their income, assets, debts, and credit history, will play a significant role in determining their ability to qualify for a new mortgage after the division of mortgage-related assets in a divorce. Consulting with a mortgage advisor or lender can provide more personalized guidance based on their specific circumstances.

The division of mortgage-related assets can affect each spouse's ability to qualify for a new mortgage in the following ways 

1. Refinancing the mortgage to a new loan in one spouse’s name releases the other spouse from responsibility for that mortgage when their name is removed from the loan.

2. Selling the home and splitting the profits.

3. If one spouse keeps the home and doesn’t have enough equity to do a cash-out refinance or the money to pay the other spouse their share, a home equity line of credit (HELOC) or home equity loan might be an option.

4. If the couple has equity in the home, the spouse keeping the house could apply for a cash-out refinance to pay their ex-partner their share.

5. Co-owning a house after divorce may be a workable solution in some situations.