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)

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.

No definition available.

Name:	star_GeneralAndAdministrativeExpenseAllocated
Namespace Prefix:	star_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration