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Related Party Transactions (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Related Party Transaction [Line Items]      
Cash distribution directly to related party $ 20.4 $ 21.4  
Cash distribution on behalf of related party to third party 4.2 3.4  
Accounts payable      
Related Party Transaction [Line Items]      
Accounts payable, trade, related parties 2.2 1.3  
Tax receivable agreement, related parties 0.3    
Other liabilities      
Related Party Transaction [Line Items]      
Tax receivable agreement, related parties 10.2 10.9  
Allocated expense | Selling, general and administrative expenses      
Related Party Transaction [Line Items]      
Expenses from transactions with related party     $ 12.6
Separation costs | Selling, general and administrative expenses      
Related Party Transaction [Line Items]      
Expenses from transactions with related party 0.2 1.9 6.7
Master services agreement fees | Selling, general and administrative expenses      
Related Party Transaction [Line Items]      
Expenses from transactions with related party 2.2 2.2  
Share-based payment arrangement | Selling, general and administrative expenses      
Related Party Transaction [Line Items]      
Expenses from transactions with related party 2.6 3.9  
Purchases and royalties paid | Cost of Goods Sold      
Related Party Transaction [Line Items]      
Expenses from transactions with related party $ 1.0 $ 0.6 $ 0.0