While its not my Dream device, the Samsung NOTE's are a "noteworthy" mention over and over again. Its the N9-that-never-was.

For this reason, I think we should ponder about what Samsung has in store next.
What will the NOTE successor be like?
More specifically, how large will its body and screen be?

Looking at how the NOTE 1 represented the SGS2.
Looking at how the NOTE 2 represented the SGS3.
And looking at the SGS4... we can make some guestimations about the NOTE 3.

The S3 (to S4) increased in screen size by 4.2% or by 0.2 inches.
If we assume the same, Note 3 screen could be increased to 5.73inches (%) or 5.70 inches.

The S3 (to S4) dimensions decreased by:
-length (136.6 both) = 0% or by 0mm
-width (69.8 vs 70.6mm) = 1.2% or by -0.8mm
-thinness (7.9 vs 8.6mm) = -8% or by -0.7mm

Note 3 dimensions could be (%):
151.1 x 79.5 x 8.6 mm
Note 3 dimesnions could be (by mm's):
151.1 x 79.7 x 8.7 mm

If you think this is impossible (a larger screen, a smaller body)... you'd be dead wrong.
The screen's dimensions are (at max) 126.9 × 71.4 mm.
Hence, it would leave a space of (at least) 12.1 × 4.0 mm for the bezels on either side.