How do I center a UIImageView within a full-screen UIScrollView?

Have you checked out the UIViewAutoresizing options?

(from the documentation)

UIViewAutoresizing
Specifies how a view is automatically resized.

enum {
   UIViewAutoresizingNone                 = 0,
   UIViewAutoresizingFlexibleLeftMargin   = 1 << 0,
   UIViewAutoresizingFlexibleWidth        = 1 << 1,
   UIViewAutoresizingFlexibleRightMargin  = 1 << 2,
   UIViewAutoresizingFlexibleTopMargin    = 1 << 3,
   UIViewAutoresizingFlexibleHeight       = 1 << 4,
   UIViewAutoresizingFlexibleBottomMargin = 1 << 5
};
typedef NSUInteger UIViewAutoresizing;

This code should work on most versions of iOS (and has been tested to work on 3.1 upwards).

It's based on the Apple WWDC code for PhotoScroller.

Add the below to your subclass of UIScrollView, and replace tileContainerView with the view containing your image or tiles:

- (void)layoutSubviews {
    [super layoutSubviews];

    // center the image as it becomes smaller than the size of the screen
    CGSize boundsSize = self.bounds.size;
    CGRect frameToCenter = tileContainerView.frame;

    // center horizontally
    if (frameToCenter.size.width < boundsSize.width)
        frameToCenter.origin.x = (boundsSize.width - frameToCenter.size.width) / 2;
    else
        frameToCenter.origin.x = 0;

    // center vertically
    if (frameToCenter.size.height < boundsSize.height)
        frameToCenter.origin.y = (boundsSize.height - frameToCenter.size.height) / 2;
    else
        frameToCenter.origin.y = 0;

    tileContainerView.frame = frameToCenter;
}