Does each mode resolved to their respective roots as modes are to be seen as nothing more than another degree of the same scale/key. Or do they always resolve to the root note of the respective major or minor key? For example, If i begin with the 4th scale degree, the lydian mode of C major would the melody resolve to F or back to C?
F would be considered the "root" or tonal center, if you call the piece Lydian. If it resolves to C then it would be an Ionian work.
Most would tend to gravitate towards the modal centre. Dorian, Lydian and Mixolydian certainly do, and obviously Aeolian does,as borne out by many works in natural minor, although sometimes helped by that raised leading note!
Locrian is the sticky one, but there aren't many examples of it, funnily enough. Having said all that, I often feel, in a modal work, that it will eventually end in the mother key (Ionian), but it needs help to stay modal by clever use of cadences and harmony.