What does a quarter break over a note mean in a piece that is suppose to be solo?

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Bar 1
Second half-note (D) is played on 2nd beat and hold without release till the end od bar. On 3rd beat, first note is released and 3rd note played without release of 2nd note.

Bar 2
Same as bar 1

Bar 3 and 4
All clear

Bar 5
First note (D) is played and hold for 3 beats throughout the bar, on 3rd beat F# joins, but D stays on.

Edit:
I would expect notation with ties for this purpose. I saw notation with breaks like this when some notes in staff are supposed to be played with other hand. White this may be the case for bar 1 and 2, in bar 5 interval is too big for most people to be grasped with one hand. 

Edit2:
I assumed this is piano sheet....Show more