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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 9 Months Ended
Mar. 31, 2015
Mar. 31, 2015
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Intrinsic values of stock options exercised $ 32.9us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised $ 68.9us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised
Outstanding "in the money" stock options using current period closing stock price $ 55.01us-gaap_SaleOfStockPricePerShare $ 55.01us-gaap_SaleOfStockPricePerShare
Shares, outstanding 5.0us-gaap_SharesOutstanding 5.0us-gaap_SharesOutstanding
Outstanding "in the money" stock options aggregate intrinsic value 159.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue 159.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue
Stock options outstanding, weighted-average remaining contractual life   6 years 4 months 6 days
Stock options exercisable 5.0us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions 5.0us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeNumberOfExercisableOptions
Time-Based Restricted Stock Units [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Fair value of restricted stock units 3.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
3.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
Share price $ 55.01us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
$ 55.01us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
Shares 2.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
2.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
Aggregate intrinsic value 126.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
126.3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= br_TimeBasedRestrictedStockMember
Performance-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_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
0.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
Share price $ 55.01us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
$ 55.01us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
Shares 0.9us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
0.9us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
Aggregate intrinsic value $ 47.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember
$ 47.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= br_PerformanceBasedRestrictedStockMember