Fair Value Measurements - Schedule of Assets and Liabilities Measured at Fair Value on a Recurring Basis (Details) - USD ($) $ in Millions	Sep. 30, 2025	Sep. 30, 2024
Liability [Abstract]
Equity Securities without Readily Determinable Fair Value, Amount	$ 29.0
Sponsored funds and separate accounts [Member]
Assets [Abstract]
Investments, at fair value	809.6	$ 509.1
Investment related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value	288.1	271.6
Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value	81.8	57.3
Fair Value, Recurring [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	1,150.5	838.0
Liability [Abstract]
Contingent consideration liabilities	20.4	28.2
Liabilities, Fair Value Disclosure	214.1	206.3
Financial Instruments Sold, Not yet Purchased, Derivatives and Other Contracts	193.7	178.1
Fair Value, Recurring [Member] \| Level 1 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	729.7	552.9
Liability [Abstract]
Contingent consideration liabilities	0.0	0.0
Liabilities, Fair Value Disclosure	193.7	178.1
Financial Instruments Sold, Not yet Purchased, Derivatives and Other Contracts	193.7	178.1
Fair Value, Recurring [Member] \| Level 2 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	317.9	168.5
Liability [Abstract]
Contingent consideration liabilities	0.0	0.0
Liabilities, Fair Value Disclosure	0.0	0.0
Financial Instruments Sold, Not yet Purchased, Derivatives and Other Contracts	0.0	0.0
Fair Value, Recurring [Member] \| Level 3 [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	4.0	7.8
Liability [Abstract]
Contingent consideration liabilities	20.4	28.2
Liabilities, Fair Value Disclosure	20.4	28.2
Financial Instruments Sold, Not yet Purchased, Derivatives and Other Contracts	0.0	0.0
Fair Value, Recurring [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	98.9	108.8
Liability [Abstract]
Contingent consideration liabilities	0.0	0.0
Liabilities, Fair Value Disclosure	0.0	0.0
Financial Instruments Sold, Not yet Purchased, Derivatives and Other Contracts	0.0	0.0
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member]
Assets [Abstract]
Investments, at fair value	809.6	509.1
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| Level 1 [Member]
Assets [Abstract]
Investments, at fair value	463.9	306.3
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| Level 2 [Member]
Assets [Abstract]
Investments, at fair value	305.2	157.4
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| Level 3 [Member]
Assets [Abstract]
Investments, at fair value	2.2	5.2
Fair Value, Recurring [Member] \| Sponsored funds and separate accounts [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	38.3	40.2
Fair Value, Recurring [Member] \| Investment related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value	288.1	271.6
Fair Value, Recurring [Member] \| Investment related to long-term incentive plans [Member] \| Level 1 [Member]
Assets [Abstract]
Investments, at fair value	253.4	242.5
Fair Value, Recurring [Member] \| Investment related to long-term incentive plans [Member] \| Level 2 [Member]
Assets [Abstract]
Investments, at fair value	3.3	0.0
Fair Value, Recurring [Member] \| Investment related to long-term incentive plans [Member] \| Level 3 [Member]
Assets [Abstract]
Investments, at fair value	0.0	0.0
Fair Value, Recurring [Member] \| Investment related to long-term incentive plans [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	31.4	29.1
Fair Value, Recurring [Member] \| Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value	52.8	57.3
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| Level 1 [Member]
Assets [Abstract]
Investments, at fair value	12.4	4.1
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| Level 2 [Member]
Assets [Abstract]
Investments, at fair value	9.4	11.1
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| Level 3 [Member]
Assets [Abstract]
Investments, at fair value	1.8	2.6
Fair Value, Recurring [Member] \| Other equity and debt investments [Member] \| NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	$ 29.2	$ 39.5

Fair value portion of asset recognized for present right to economic benefit.

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Amount of liability recognized arising from contingent consideration in a business combination.

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Fair value of obligations arising from derivatives and other contracts sold short.

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Fair value of financial and nonfinancial obligations.

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Amount of investment in debt security measured at fair value with change in fair value recognized in net income (trading) and investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).

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