Well, the answer to this seemingly simple question can be complicated, as some of the posts in response have indicated. Let's take the NEC first.
1) The trackage from South Station to the Rhode Island line is actually owned by Massachusetts, dispatched and maintained by Amtrak,
2) From the state line to New Haven, it's all Amtrak.
3) New Haven to New Rochelle is owned and maintained (and dispatched) by Metro-North. From there to DC, it's all Amtrak, except that LIRR and Amtrak operate Penn Station on alternating six-month shifts.
4) New Haven to Springfield is Amtrak.
5) New York to Albany is complicated. The West Side Connection is Amtrak owned and dispatched, then trains use Metro-North to Poughkeepsie (MP 75.8). From there, it's CSX all the way to Albany, although the State of NY pays for a higher track class than CSX would otherwise maintain. Trackage from CP 125 into Albany is owned by CSX, but maintained by Amtrak, as is the track to Schenectady. Beyond to Amsterdam, the state of NY owns and Amtrak dispatches. The Post Road Connection is Amtrak owned and operated.
6} The Harrisburg Line is owned and operated by Amtrak.
Outside the NEC, yes, Amtrak owns and dispatches only the Porter to Kalamazoo segment, and some terminals including Chicago and Portland. But Amtrak does run on several segments of state-owned track dispatched by commuter rail operators. The San Diego line has already been mentioned. Amtrak 3 and 4 usually use the San Gabriel Sub from San Bernardino to LAX. It belongs to Metrolink. Amtrak 1 and 2 also use part of the San Gabriel.
Amtrak Florida trains to Miami use a segment owned by the state of Florida between West Palm Beach and Miami. There is talk about moving the Eagle to the TRE (former Rock Island/Burlington) between Dallas and Ft. Worth. While Metra in Chicago does own track, all Amtrak operations in the area are over Class I trackage.
As to terminal switching roads, yes, Amtrak operates over NOPB to get across the Mississippi. In Minneapolis, Amtrak uses Minnesota Commercial to get from the CP to BNSF. Midway Station is actually on Minnesota Commercial trackage. In Portland, OR Amtrak owns the Portland Terminal Company. In St. Louis, Amtrak uses TRRA to get to the Amtrak station (on either of the two routes a train might take). In Kansas City, the BNSF main line that Amtrak uses actually belongs to Kansas City Terminal, which is jointly owned by BNSF, UP, and KCS but runs no trains itself. Gateway Western (now KCS) provides contract switching services for KCT.
There are probably a few other oddities that others can point out on this subject. That's all I can think of.
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