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A half diminished resolving a tone downwards: D half diminished to C major? To me this is as strong as a V I ?

Diminished and half diminished chords are very powerful. If you take any diminished chord and build a major scale from each note of the chord, then you have four major escales that have lots of interesting relationships beetwen them throug relative and parallel minors.

Why ii half dm to I major works well, i don't know specifically, but it may be working slightly as secondary dominant, or as a V with some altered notes, besides it has the b flat, wich makes C dominant. When you have dominant and diminished chords floating around, you sure will have interesting sounds.

(If you ask this question in the non classical forum, the jazz wizzards will give a much deeper answer).

I'm sorry, there's no b flat in d half dm.

I'm musing it has something to do with the parallel minor (Cm), the D half dim. is the second mode of C minor. Often a minor tune will resolve to a parallel major,

Agreed - this topic is well-suited to that forum, where many similar topics abound:

http://forum.pianoworld.com/ubbthreads.php/forums/35/1/pianist-corner-non-classical.html

It is exactly because of that that it works so well.

It is made up of D-F-Ab-B. Therefore, it is the same as the dominant VII chord with the Ab replacing the G. As in the dominant VII chord, B is the leading note rising to the tonic C and the F falls to the third of the tonic chord. Bingo!

As a composer I've used descending semitone harmony often and that's why this progression works so well. The F and Ab resolve down by half steps to E and G, the C stays the same and the D can resolve either up or down to C or E. It's similar to the resolution of a Neopolitan chord except it works even better in a major key.

Okay, from a jazz player’s perspective the d half-diminished has the notes of a G7sus(b9) without the G itself. Add a G in the bass and you’ll hear it. This is a Dominant 7th sus chord going to the tonic without the 4 first resolving to the 3.