In the 50's the LIRR sold the ROW to the NYC Transit Authority. Originally, they were going to take over the entire ROW, but since limited funds were available, they only did it from the Liberty El, however did own the whole ROW.
Of course eventually, the MTA took over both the LIRR and the NYCTA. IINM, I think I remember hearing that currently the City of New York or NY State owns the ROW, not LIPA or something like that.
An interesting note is that since the subway was to take over the entire Rockaway ROW, the line was never "officially" abandoned when the LIRR stopped operations in 1962. That is why the tracks and third rail were never pulled up. It was never "officially" abandoned, just put "out of service".