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Basis of Presentation and Principles of Consolidation (Basis of Presentation) (Details) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Sep. 30, 2022 | Sep. 30, 2023 | Sep. 30, 2022
General and administrative expenses allocated from iStar | $ 7.0 | $ 14.1 | $ 5.9
Interest expense allocated from iStar | 9.5 | 8.0 | 33.3
General and Administrative |  |  |
Stock-based compensation expense allocated from iStar | $ (0.2) | $ 1.8 | $ (13.2)

X
- Definition The aggregate total of expenses of managing and administering the affairs of an entity, including affiliates of the reporting entity, which are not directly or indirectly associated with the manufacture, sale or creation of a product or product line allocated from iStar. + References No definition available. + Details
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Namespace Prefix: | star_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Amount of the cost of borrowed funds accounted for as interest expense allocated from iStar. + References No definition available. + Details
Name: | star_InterestExpenseAllocated
Namespace Prefix: | star_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Amount of expense for award under share-based payment arrangement allocated from iStar. + References No definition available. + Details
Name: | star_StockBasedCompensationExpenseAllocated
Namespace Prefix: | star_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Details
Name: | us-gaap_IncomeStatementLocationAxis=us-gaap_GeneralAndAdministrativeExpenseMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |