How to animate the frame of an layer with CABasicAnimation?

The frame property of a CALayer is a derived property, dependent on the position, anchorPoint, bounds and transform of the layer. Instead of animating the frame, you should instead animate the position or bounds, depending on what effect you are trying to accomplish.

To move a layer, you can animate the position:

-(void)moveLayer:(CALayer*)layer to:(CGPoint)point
{
    // Prepare the animation from the current position to the new position
    CABasicAnimation *animation = [CABasicAnimation animationWithKeyPath:@"position"];
    animation.fromValue = [layer valueForKey:@"position"];

    // NSValue/+valueWithPoint:(NSPoint)point is available on Mac OS X
    // NSValue/+valueWithCGPoint:(CGPoint)point is available on iOS
    // comment/uncomment the corresponding lines depending on which platform you're targeting

    // Mac OS X
    animation.toValue = [NSValue valueWithPoint:NSPointFromCGPoint(point)];
    // iOS
    //animation.toValue = [NSValue valueWithCGPoint:point];

    // Update the layer's position so that the layer doesn't snap back when the animation completes.
    layer.position = point;

    // Add the animation, overriding the implicit animation.
    [layer addAnimation:animation forKey:@"position"];
}

To resize a layer, you would animate the bounds parameter:

-(void)resizeLayer:(CALayer*)layer to:(CGSize)size
{
    // Prepare the animation from the old size to the new size
    CGRect oldBounds = layer.bounds;
    CGRect newBounds = oldBounds;
    newBounds.size = size;
    CABasicAnimation *animation = [CABasicAnimation animationWithKeyPath:@"bounds"];

    // NSValue/+valueWithRect:(NSRect)rect is available on Mac OS X
    // NSValue/+valueWithCGRect:(CGRect)rect is available on iOS
    // comment/uncomment the corresponding lines depending on which platform you're targeting

    // Mac OS X
    animation.fromValue = [NSValue valueWithRect:NSRectFromCGRect(oldBounds)];
    animation.toValue = [NSValue valueWithRect:NSRectFromCGRect(newBounds)];
    // iOS
    //animation.fromValue = [NSValue valueWithCGRect:oldBounds];
    //animation.toValue = [NSValue valueWithCGRect:newBounds];

    // Update the layer's bounds so the layer doesn't snap back when the animation completes.
    layer.bounds = newBounds;

    // Add the animation, overriding the implicit animation.
    [layer addAnimation:animation forKey:@"bounds"];
}

You can combine these animations using a CAAnimationGroup if you need to move and resize a layer at the same time.