The exact owners of abandoned rail lines in the US varies from place to place, and depends upon the details of how the line was acquired in the first place. When the lines were built, rights to construct a right of way were acquired from various land owners by various means, and while some might have been build on right of ways with the 20 foot width that cascaderailroad suggests, in my experience, in most cases the rights of way were considerably wider, often 100 feet in width. Some of these were purchased, some were given by the US government in the form of land grants, others were leased from the property owners. When rights of way were abandoned, some properties reverted to the succesors to earlier owners, some which had been owned by the railroads were acquired by other entities. In Dallas / Fort Worth Texas, for example, many miles of right of way owned by the large railroads were acquired by the Dallas Area Rapid Trasit (DART) agency, which still owns the rights of way, and leases portions to freight railroads.
The question really cannot be answered in any other general way; to find out the status of ownership of any particular bit of abandoned railroad right of way, one really needs to research the deed to the property, and find out the status. The status can be different from parcel to parcel, even when the parcels adjoin.
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