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Based on the current positions of teams and assuming they finish the season ending in said position (and get the same draft positions), this is who I think the top 10 drafting franchises should take based on need and talent, in reverse order:
turner
clippers10. LA Clippers: Wesley Johnson
Several players have fallen by this time and Johnson lovers will be starting to hate, but this is an ideal destination for Johnson as he can come in and be of use straight away. Lets also be real, Rudy G and LeBron aren't coming to LAC so unless the Clipps can snare Evan Turner somehow, then this guy is the next best thing. Several other top 5 prospects are still available, but With Griffin and Kaman ready to go next season, and with reliable backups in Jordan and Smith in the wings, the Clipps are pretty much set for bigs at this time.

Utah_Jazz_logo9. Utah Jazz: Donatas Montejunas
Ok, the truth: Okur is getting old... and Montejunas is probably an upgrade on Okur anyway.
Sloan loves continuation and this will mean he's basically not changing his squad in the future.

sacramento_kings_logo18. Sacramento Kings: Hassan Whiteside
Sacramento are technically "set" at every position now that K-Mart has been traded, but a player of Whiteside's calibre wouldn't be passed on draft night. Keep in mind also that Paul Westphal is known for getting the project players up and going better than most (see Ceballos, Dumas et al.) and Whiteside offers some major defensive grunt which this team lacks.
He'd also be a great fit in the Landry/Thompson/Hawes trio and may even get Hawes to actually take this whole caper seriously.

76ers7. Philadelphia 76ers: Jan Vesley
This is based on the roster "staying the same" which we all know won't happen.  Even if Iggy and Dalembert go though, Philly have Jason Smith and Speights waiting in the wings to backup Brand so my thinking is that Ed Davis and Greg Monroe won't offer much to this team.
Vesley on the other hand provides something any coach running a Princeton offense needs - a floor spacer. He can play the 3/4 and create match-up headaches whilst allowing Brand to get single coverage in the low block.
Helping straight away could also be a good thing, and Vesley can do that.

pistons6. Detroit Pistons: Al Farouq Aminu
Lets be honest, Detroit are going to have a clearing sale this off-season.
Dumars has realised some dumb moves, but also seen some hope of future success closer than many expect. Whilst Aminu is a project, he can develop well under the tutelage of the plethora of veterans that Detroit posses. Then in 2/3 seasons watch out - this guys has a bigger wing span than Durantula ALREADY for the same height.

Wizards5. Washington Wizards: Cole Aldrich
Since losing Jamieson Washington have realised that they have a super-talented PF in Andray Blatche. Al Thornton can also be effective when given minutes...
The problem for me, for this team, is their situation at the 5. McGee is consistently inconsistent and doesn't seem to be making the most of his minutes. Aldrich has the frame of a Kevin Love type which is exactly what Washington need to go alongside Blatche, hence why I bumped him up here.

pacers4. Indiana Pacers: Derrick Favors
The Pacers need a strong big to go alongside Roy Hibbert and although Favors is offensively very raw, he promises to develop into quite a defensive specialist in the future.
I wanted to put Ed Davis here but we know how GM's react to injuries... I'll also throw out here that Indiana could grab Vesley or Montejunas here as they love Bird-look-alikes...

warriors3. GSW: DeMarcus Cousins
The guy is a beast, can play the running game (as he's proven at UK), and is exactly what the Warriors need. This is most likely the exact reason why the Warriors won't pick him and will grab a shooting guard instead...

twolves2. Minnesota Timberwolves: John Wall
They'll be hoping Turner falls here, but who could be disappointed in getting Wall?
Furthermore, you can't pass on this kind of talent - even if it means pushing the rebuilding back a couple of years. If Wall comes in then Flynn will be traded and Rubio, a true PG, will be brought over ASAP.
Wall/Rubio/Love is a nice core to start off with, and the Flynn (and some say Jefferson) trade should bring in something decent in return as well.

nets1. New Jersey: Evan Turner
Yep I think they should go with Turner, Lopez, Lee and Harris and see what happens.
Shipping Harris would be next to impossible and a bit of a stretch given Wall isn't a true PG (not that Harris is either). Turner is the most well-rounded player in the draft, and probably an equivalent of a Tyreke Evans with the exception that he prefers to play 2/3 positions. Long-term he has Brandon Roy written all over him.