I'm Holland and its 1530, I've sent some 9000 guys on a blind oversea expedition and they have landed on some New World territory filled with that curious little with puffy plant known as cotton. Because its only inhabited by primitives we just seized their land so now Holland with its only 2 continental provinces, owns 7 oversea province in North America. Neither my trade range or colonial range can reach those lands of course. So what will happens now ? Will I still be able to trade cotton from america to Lubec where it says its going ? Should I build a new CoT in the new world ? In Holland ? I don't understand enough the trade mechanisms to clearly see where I'm going.
Yes, trade value of provinces getting to CoTs is not affected by trade range so the listed CoT will get the value of the trade. Trade range only affects where you can send merchants to trade.
It wouldn't be the worst idea in the world to build a CoT in the new world (and also move your capital there) although you may have difficulty doing so any time soon. As soon as you leave the Hanseatic League the trade map re-shuffles and it is pretty unlikely the CoT your provinces will land in has enough value to allow a build (you can't build a CoT while in a trade league). A more realistic option would be to find and capture the existing CoT in the new world (it is pretty unlikely there isn't one). This will have a negative impact on your trade chance until the province becomes a core though.
Note that you can't build a CoT in a non-core province so in any case it will take a while for you to be able to do so in the new world. Building one in Holland wouldn't be particularly effective in the long run unless you about-face the sliders and go mercantalist as your free trade setting decreases the chance your provinces will bypass closer CoTs to trade in yours.