First, I assume you mean "transcontinental railroad". Much of the route is still in use. The eastern chunk is still owned by the Union Pacific Railroad. The western chunk was originally owned by the Central Pacific Railroad, which was bought by the Southern Pacific Railroad, which merged in the 1990s with the Union Pacific. The route has been changed in places--the meeting point at Promontory Summit was bypassed, for example. The general route is still in use, though.

Did the tracks that met at Promontory Summit constitute the whole of the line, or where their companion tracks nearby?

I'm not sure what you mean by this. At the time there was no other transcontinental route--if you wanted to go coast-to-coast, you had to go through where the lines had met in Utah. But you couldn't do it anyway at first, since there were gaps in the system caused by rivers even when the railroad was formally complete.