I think the point of interest here isn't really the question, if "earth" will demand taxes or not. It's just a sub-question of a much more bigger
topic. Namely the question how mankind will manage the way, how colonies will be administrated and which kind of power structure will therefor
evolve.
There are many interesting points belonging to this question but for the sake of simplicity let's break it down to some main aspects:
First of all there would be two different types of colonies:
a) colonies within our solar system and
b) well, you know...other stars
As for
a) there will be a big dependency on supplies and support from Earth in the beginning of course. Thus these first colonies will widely
stay under the control of several nations, private companies etc.
(Many models would be thinkable here. The least one i'd expect is a kind of "unite world" control. Most probably there will be a struggle
even between certain nations ... as always but i said let's keep it simple for now)
Here we have a break even point i think. The type of the political system, that we will have in future ventures, when colonies in other solar systems
will be founded, greatly depends on two major key aspects. The way how we will deal with colonies in our own solar system and the technique that we
will have, when we spread our seeds to other star systems.
This leads me to
b). The first settlers of an exo-planet will emerge out of a certain political system within our own solar system. Meaning
they will be part of it and thus will also represent it. When they finally found their new home(s) they will establish a community that represents the
political system, they lived in.
Of course after some decades there might come a change and here's the second break even point. Now the above mentioned technique is the next key
aspect. Can we communicate with them in a "faster-then-light" way or do we need to wait like 100 years before an order has reached the system and
another 100 to receive the message?
I think the question here isn't if "Earth" could back up the power with ships and stuff to keep the control over the exo-colonies. The question is if
the technology of FTL-messaging will be available when such a mission first starts to another solar system or not. If not, well then the whole mission
will most probably planned as a self sufficient colony without keeping some kind of control over them.
If yes then the whole mission could be planned in a way like we plan our space missions today:
"Houston, we found walking plants here on Gliese581d! What shall we do?"
"Erm, did you just say "walking plants" ? Well, explain them, that we earthlings don't like, when our potatoes go out for a walk. Use your beam
weapons to emphasise your point. Housten over."
"Copy that!"
edit on 14-7-2014 by Tichy because: (no reason given)