Personally, I think centre control is highly exaggerated. Also, its difficult not to control centre with aleast one pawn or piece, given that any movement of any piece will end up controlling the centre. So, I don't know why people make it into some kind of an important principle of chess.
Centre control - essential principle or just a dogma?

b) is my answer and probably same for most others. Like any opening principle, you don't have to stick to it all the time.
True, I think controlling space is important where the action is happening and the space near 2 kings.

Center control is a heuristic, so like any heuristic there exist exceptions. However, it is an extremely reliable heuristic: even hypermodernism recognizes the need to challenge the center, certainly putting a knight on the rim is usually foolish, Nimzovitch's first chapter of "My System" gives many examples of how the center is easily overrun by a pawn advance if the opponent fails to advance a center pawn to at least his 3rd rank, and how many tic-tac-toe players do you know who *don't* start by marking the center square first?

Of course it is important. However, I'll pick a c) answer because at my level it's more about the blunders...

The center is absolutely essential to winning games. Controlling it just means you are doing better. But all legitimate openings involve at least a plan to attack the center. Any reasonably decent player will steamroll his opponent if allowed complete control of the center (Providing he doesn't start dropping pieces or give up king safety). Just because you get away with letting your opponents control the center doesn't mean the center is useless. It just means it wasn't used properly.

Also, your poll is erroneous because it only applies to games that end immediately after the opening. Controlling the center isn't always the cause of winning or losing, it's just a strong positional advantage. Nobody *Always* wins because they play their Knights to the center. But hardly anyone ever wins if they put their Knights on h3 and a3.
I think central control is vital.
You can cede center, but it's only temporary - at some point in the middlegame, you will HAVE to strike back at the strong pawn center or be lost.
I like playing the modern defense and if you just let those central pawns roll, it's game over. You HAVE to strike back at the center with c5 or f5 at some point, and maintain pressure on the center with the fianchettoed bishops.
Weirdly enough though, the main lines for the modern defense as white, after occupying the center with pawns are pure flank pawn attacks - a2,a3,h2,h3, and pretty early on. But this does make sense since the center is occupied by wihte's pawns before this.

Central control is vital. Is it an absolute? I know my pieces are more active when they are centralized. And piece activity is the name of the game.
In blitz where calculation need to be quick, to do a quick evaluation of a future position, I often look at the balance of control in the 4 center squares. If, for example, my opponent owns 3, while the last one is contested (and otherwise the position seems even) I can quickly discard the idea. (I use this during the first 15 moves lets say, when deciding how to set things up.)
There are of course lots of things that go into properly evaluating a position, but that this criteria of mine has been so useful in the past I think is interesting.
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Anyway, this is a good question to try to figure out for yourself. A million people can tell you the center is important, but unless you understand why you'll probably incorrectly evaluate it in your games... so this is a good one to think for yourself.

Center control is a heuristic, so like any heuristic there exist exceptions. However, it is an extremely reliable heuristic: even hypermodernism recognizes the need to challenge the center, certainly putting a knight on the rim is usually foolish, Nimzovitch's first chapter of "My System" gives many examples of how the center is easily overrun by a pawn advance if the opponent fails to advance a center pawn to at least his 3rd rank, and how many tic-tac-toe players do you know who *don't* start by marking the center square first?
+1

Exactly. Its not always the centre. Sometimes flanks are more important because all the action is happening there. Its like controlling Africa while the action is happening in Asia.

what part of the board would you try to control if not the center??
I would try to control as much space as I can. But, I think the critical areas to control would be:
a) where the action is happening i.e. where pieces are under attack or in contract.
b) my king.
c) opponent king.

In blitz where calculation need to be quick, to do a quick evaluation of a future position, I often look at the balance of control in the 4 center squares. If, for example, my opponent owns 3, while the last one is contested (and otherwise the position seems even) I can quickly discard the idea. (I use this during the first 15 moves lets say, when deciding how to set things up.)
There are of course lots of things that go into properly evaluating a position, but that this criteria of mine has been so useful in the past I think is interesting.
----
Anyway, this is a good question to try to figure out for yourself. A million people can tell you the center is important, but unless you understand why you'll probably incorrectly evaluate it in your games... so this is a good one to think for yourself.
Actually, it seems to me that its difficult not to control the centre in some way or the other. All your pieces have to be on the edges of board, to not control the centre. So, almost everyone always will control centre in some form or the other. So, I don't know how something that will happen anyways is made into an essential principle. And it seems to me that if you place too much importance on the centre rather than look for the key areas in the position, then you will waste too many resources in controlling a useless centre which would be in reasonable control anyways even if you don't try to control it.

K-side & q-side flanks & center. Bishops can't really hit the flanks unless they pass through the center or bypass a locked center. A breakthrough indicates a lock. A lock indicates control. A breakthrough on any side assuming lots of active pieces on the board requires speed of advance and slowing down enemy advance on the other sides, requiring some form of control. So is center control required in a k+knightpawn vs k? No.
There, I've managed to write complete gibberish. made sense to me when I was writing it though ...

K-side & q-side flanks & center. Bishops can't really hit the flanks unless they pass through the center or bypass a locked center. A breakthrough indicates a lock. A lock indicates control. A breakthrough on any side assuming lots of active pieces on the board requires speed of advance and slowing down enemy advance on the other sides, requiring some form of control. So is center control required in a k+knightpawn vs k? No.
There, I've managed to write complete gibberish. made sense to me when I was writing it though ...
If the centre is locked, its locked for both sides. And you just have to find an alternate way. If its open, then its open for both sides. Both sides can use the open centre.

May vs can vs did. Defeat vs victory.
True. But, the point under debate is: is the centre control vital or necessary? Is it something that you have to do actively by putting lot of resources or is it something that will just happen by itself even if you don't care about it.
I have stopped caring about centre control for a long time and it doesn't seem to have had any impact on my games simply because the centre control will happen automatically even if you don't care about it.
Is controlling the centre really important? Or is its importance highly exaggerated? Plz discuss.
Also, a poll:
has centre control helped you in winning games?
a) Yes, centre control has played a crucial role in winning or losing my games.
b) sometimes but not always.
c) rarely.