To begin with, know that I enjoy Cosmology, but Havn't a clue about
what I read means beyond the laymen explanations.  Here goes anyway.

In all directions, expansion per Hubles Constant.  If two objects
exist, one 100 light years to the left, and one same distance to the
right, they are both moving away at the same rate.  Now add two more. 
So a total of five objects, us in the middle.  The object to the
immediate left sees us to the right, and another to the left 100 light
years to the left.  Both of them expanding at the same rate away.  So
no matter where you are, objects appear to be moving away from you. 
(Not including local objects)

So, can I conclude that no matter where you are, you are stationary to
everything else, and that no matter where you are, you are the center
of the univers?

Since I know the answer (although It makes no sense to me) I ask the
bigger question:

Isn't god spreading himself kind of thin?  No, just kidding.

What I want to know is this.  In any direction you look, are you not
bound to find objects moving a relativistic velocities?  What effect
does this speed have on such massive objects with respect to their
gravity, as in high speed motion increasing or appearing to increase
mass.

Yes you are correct -- it is allowable in Einstein's laws for
different parts of "space-time" to be moving with velocities which
differ by more than the speed of light. Objects within a given "patch"
of space-time cannot travel faster than light.

It is interesting to think about what happens when you try too look at
an object which is very far away in the Universe. The further away an
object is, the longer it takes for the light to reach you. This means
that when you look at an object a hundred light years away, what you
see is how the object looked a hundred years ago.

Interestingly, if you do the math you find that distance away in the
Universe where space-time is moving away from us at exactly the speed
of light, is exactly the distance where light takes the full lifetime
of the Universe to reach us.

If you try to look this far with modern (CMB) telescopes you find that
there aren't any stars, there's just hot gas which is opaque. This hot
gas is the explosion from the Big Bang -- in other words CMB
telescopes such as WMAP, COBE and VSA have taken pictures of the
"fireball" from the Big Bang (redshifted to longer wavelengths).

See the website:
http://www.mrao.cam.ac.uk/telescopes/vsa/images_extended.html

for some example pictures of small parts of the fireball from the Big
Bang. "Fireball" is a slightly misleading term as the "fire" was
everywhere in the Universe at the time. To see this, look at the all
sky "map" of the fireball at:
http://map.gsfc.nasa.gov/m_or.html

This map is plotted just like a "World Map", but instead of showing
the countries on Earth, it show how the light from the Big Bang is
distributed over the whole "sky" all around the Earth.

One other point I should have mentioned -- the mass associated with
the kinetic energy of an object depends on the frame of reference. A
fast moving body does not feel any heavier -- it only appears heavier
to observers moving at a different velocity.

It's all quite counter-intuitive at first sight, but comes out of a
small number of very simple equations which describe a very simple way
of looking at the Universe. It is also quite well tested
experimentally.

This news report appeared today, and is quite relevant to you
questions on the expansion of the Universe:

http://news.bbc.co.uk/2/hi/science/nature/3753115.stm

We used to have a shirt for sale in our school of engineering student
affairs office about why it's great to be an engineer.  Among other
reasons were "free cable" and what more and what not.  The number one
reason is that we're the center of the universe - we establish our own
coordinate system.

So yes, YOU are the center of the universe whenever you want to be. 
Heck, you can even say the earth is the center of the solar system and
that everything rotates around it.  You can say whatever you want -
just back it up with your coordinate system, which YOU define.  Sure,
the equations get harder, but isn't it worth the ego trip?

That's all...

All of us associated with Google answers, researchers,
non-researchers, editors and hangers on ARE the center of the universe
and we can prove it by means of concentric circles.

Cheers
digs