If you consider big bang. According to that What's left at the center of universe where the Big bang occured?
There's a very common misconception that the Big Bang happened at a point like a bomb going off. It doesn't help that almost ever TV documentary on the subject represents the Big Bang in this way. Explaining what actually happened is hard without going into the Maths, but here's an explanation I gave taken from (of all places) the Science Fiction Stack Exchange:
Imagine drawing out a grid with spacing of 1 light year. Although obviously we can't do this, you can easily imagine putting the Earth at (0, 0), Alpha Centauri at (4.37, 0) and plotting out all the stars on this grid. The key thing is that because the universe is infinite this grid is infinite i.e. there is no point where you can't extend the grid any further.
Now wind time back to 7 billion years after the big bang, i.e. about halfway back. Because the universe shrinks as we wind time back, our grid now has a spacing of half a light year, but it's still infinite - there is still no edge to it.
Now wind back to 0.0000000001 seconds after the big bang. There's no special significance to that number; it's just meant to be extremely small. Our grid now has a very small spacing, but it's still infinite. No matter how close we get to the big bang we still have a infinite grid filling all of space. You may have heard pop science programmes describing the big bang as "happening everywhere" and this is what they mean. The universe didn't shrink down to a point at the big bang, it's just that the spacing between any two randomly selected spacetime points shrank down to zero.
Incidentally, if you try to calculate the size of the universe at the big bang itself you get zero times infinity i.e. zero spacing of the grid but it's still infinitely big. We call points like these singularities because we can't tell what happened there.
So to back to your question, what was left behind by the Big bang is, well, me and you and everything we can see when we look into the night sky. Because the Big Bang happened everywhere we are all relics of the Big Bang.
The question you are asking yourself is ill defined. The universe has no center, thus you cannot ask what is there. The important thing to realize is that a singularity (presented in the Big Bang Theory) is not a physical thing, you can't say "oh look at that singularity over there"(from that point the universe started). In fact a singularity is merely a situation where our theories cease to be meaningful. The Big Bang theory says that the universe is roughly the same everywhere, so there are no special points. It's equivalent to say that the center of the universe is everywhere and nowhere.
There is a central point, the point that is the opposite to the expansion of the sphere. We can't see it, but I would assume that in a similar way to how when large stars go supernova they leave behind a black hole, and how there are black holes in the middle of galaxies, there would probably be a black hole in the centre.
We would never see it, because the light from behind it would never reach us, at least not until the universe collapses into it, in many billions of years.
The description that there is no centre is used to express an idea of the way spacetime is, but it's both right and wrong, depending on what you mean.