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Stock-Based Compensation - Summary of Incentive Equity Awards (Additional Information) (Detail) (USD $)
In Millions, except Per Share data, unless otherwise specified
3 Months Ended 6 Months Ended
Dec. 31, 2014
Dec. 31, 2014
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Intrinsic values of stock options exercised $ 17.6us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised $ 36.0us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised
Outstanding "in the money" stock options using current period closing stock price $ 46.18us-gaap_SaleOfStockPricePerShare $ 46.18us-gaap_SaleOfStockPricePerShare
Shares, outstanding 5.3us-gaap_SharesOutstanding 5.3us-gaap_SharesOutstanding
Outstanding "in the money" stock options aggregate intrinsic value 130.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue 130.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue
Stock options outstanding, weighted-average remaining contractual life   5 years 9 months 6 days
Stock options exercisable 5.3us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions 5.3us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
Performance-Based Restricted Stock Units And Time-Based Restricted Stock Units [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Fair value of restricted stock units 0.2us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockUnitsAndTimeBasedRestrictedStockUnitsMember
0.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockUnitsAndTimeBasedRestrictedStockUnitsMember
Time-Based Restricted Stock Units [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Share price $ 46.18us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_PlanNameAxis
= br_TimeBasedRestrictedStockMember
$ 46.18us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_PlanNameAxis
= br_TimeBasedRestrictedStockMember
Shares 2.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_PlanNameAxis
= br_TimeBasedRestrictedStockMember
2.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_PlanNameAxis
= br_TimeBasedRestrictedStockMember
Aggregate intrinsic value 106.1us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_PlanNameAxis
= br_TimeBasedRestrictedStockMember
106.1us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_PlanNameAxis
= br_TimeBasedRestrictedStockMember
Performance-Based Restricted Stock Units [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Share price $ 46.18us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockMember
$ 46.18us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockMember
Shares 0.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockMember
0.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockMember
Aggregate intrinsic value $ 39.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockMember
$ 39.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_PlanNameAxis
= br_PerformanceBasedRestrictedStockMember