Re-entering US: with Green Card while H1B still valid.

[mfsn]

What should I do when I re-enter the US next time I travel abroad? Should I present the Green Card, my valid H1B or both?

What about my current I-94? Do I have to turn it in next time I leave the US?

Is the non-immigrant status automatically dropped and replaced by the immigrant status effective on the day my Green Card is approved? What happens with the remaining days for which the H1B visa is still valid for?

Thanks.

 

[ginnu]

What should I do when I re-enter the US next time I travel abroad? Should I present the Green Card, my valid H1B or both?
-----Green Card and passport. H1 is nomore valid after getting GC
What about my current I-94? Do I have to turn it in next time I leave the US?
--------- if you have I-94 you can give at airline counter(if you dont give that is not problem after GC). when you enter US you dont need to fill any I-94
Is the non-immigrant status automatically dropped and replaced by the immigrant status effective on the day my Green Card is approved?
----yes
What happens with the remaining days for which the H1B visa is still valid for?
-----------not valid
Thanks.