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Units Outstanding (Details) - shares
3 Months Ended 9 Months Ended
Jul. 10, 2025
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2025
Sep. 30, 2024
Units Outstanding          
Beginning balance (in shares)       292,107,907  
Units issued (in shares)       20,979,780  
Units retired (in shares)       (20,869,292)  
Ending balance (in shares)   292,218,395   292,218,395  
Beneficial ownership of AB Holding units (in shares)       20,869,292  
Total amount of AB Holding units purchased (in shares)   100,000 1,100,000 1,300,000 2,100,000
AB Holding Units | Amended Exchange Agreement | EQH          
Units Outstanding          
Units retired (in shares) (19,682,946)        
Beneficial ownership of AB Holding units (in shares) 19,682,946        
Tender Offer | AB Units          
Units Outstanding          
Total amount of AB Holding units purchased (in shares)       35,380