Philly & Trenton in Trenton?

As far as I can tell, the Philadelphia & Trenton RR was only incorporated in Pennsylvania, and Poor's manuals clearly show that it ended at the state line.
According to http://www.prrths.com/Downloads/PRR1835.pdf the Delaware was crossed in 1837, with the railroad almost but not quite connecting to the Camden & Amboy RR Trenton Branch. In 1839 the connection to the Camden & Amboy was built.

I have a few questions:
How did the P&T get from the Delaware River to the original Trenton depot at Hanover St and Broad St?
Who built the P&T in Trenton? As far as I can tell, the P&T always officially ended at the state line; was a separate P&T chartered in New Jersey and later consolidated into the C&A?
Here's a map of the section I'm asking about:

I found a comprehensive overview of early railroad construction in Trenton. The track over the
Delaware River bridge to the depot was apparently constructed on the private property of the Trenton Delaware Bridge Company, running from the bridge down Bridge St. to Bloomsbury (Warren) St., then east to the canal, then north up the west bank of the canal to Merchant St., then west on Merchant St. to Stockton St., then north on Stockton St. to Hanover St., then west on Hanover St. to Greene (Broad) St. The Legislature decided that the P&T had no right to operate a railroad in New Jersey, but the politically powerful Joint Companies promptly procured a charter for the authority to build New Brunswick-Trenton-Bordentown with a branch to the Delaware Bridge. Horsepower was used from the depot to the Pennsylvania side of the bridge before the Camden & Amboy connection was made (presumably due to the lack of a charter?), but when the continuous route to New York was opened Jan. 1, 1839, this practice was evidently discontinued.

So I'd mark down the old bridge and the line to the west bank of the canal and then to the old depot as Trenton Delaware Bridge Company. The new bridge would presumably be P&T to the middle of the river, and United New Jersey RR on the other side of the state line, as having inherited the charter rights of the Camden & Amboy. (The new bridge was built in 1874, after the formation of the UNJRR.)