I lay two pieces of straight track from New Haven to Boston (cost 2x 2000). Then my opponent wants to connect New Haven to Providence.
Q1) To connect New Haven to Providence, my opponent pays $2000 and removes my straight track tile leaving New Haven and replaces it with one that has a spur (to the right) so that New Haven to Providence are connected while leaving my New Haven to Boston link intact?
Assuming I have Q1 understood correctly...
Q2) Who owns the new spur tile that he played? My guess is that he owns it when it is being use for deliveries to Providence, but that I own it when it is being used for deliveries to Boston
There are no spur tiles in RRT. Each tile has either one or two pieces of completely independent track on them. Each piece of track enters one hex and exits another (i.e. in a tile with two pieces of track, there are four hexsides with track leading to them). In tiles with a crossover, the tracks do not connect.
There is no way for a situation to arise where the ownership of any link is in question.