According to reports in the Russian media, Prime Minister Putin has demanded in a very harsh manner that the Minister Of Defense Serdiukov present him with a detailed report about the scandal at the training center at Ryazan Airbone School. According to rumors, the current Chief of General Staff, General, Nikolai Makarov, is likely to replace Serdiukov.
If true, Makarov would be a strange choice since it appears that he was the author of the idea to subordinate the Airborne Forces to the High Command of the Ground Forces.
Other sources report that the plans to create a separate branch of Special Operations Forces, a la USSOCOM, have been abandoned.  If true, that would mean that the GRU would keep the control of the Spetsnaz Brigades and the Airborne Forces would keep the Independent 45th Regiment of the Airborne Forces.

These fully of (still unconfirmed) rumors appear to indicate that a very serious bureaucratic battle is taking place behind the scenes and that the recent leaks in the Russian media are part of a PR strategy used by some (Shamanov?  Putin?) to score political points at the expense of their political opponents (Medvedev?  Serdiukov?)
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FYI: this is, according to Dmitry Gorenburg, the current structure of the Russian Airborne Forces:
* 7th Airborne Division (Novorossiysk, Krasnodar Krai, North Caucasus MD)

o 108th Airborne Regiment
o 247th Airborne Regiment (Stavropol)
o 1141st Artillery Regiment (Anapa, Krasnodar Krai)
o 3rd Air Defense Regiment
o 162nd Reconnaissance Company
o 309th Engineering Company (Temryuk, Krasnodar Krai)
o 743rd Communications Battalion
o 6th Maintenance Battalion
o 1681st Logistics Battalion

* 76th Airborne Division (Pskov, Leningrad Military District)

o 23rd Airborne Regiment
o 104th Airborne Regiment
o 234th Airborne Regiment
o 1140th Artillery Regiment
o 4th Air Defense Regiment
o 656th Engineering Battalion
o 728th Communications Battalion
o 7th Maintenance Battalion
o 1682nd Logistics Battalion

* 98th Airborne Division (Ivanovo, Moscow Military District)

o 217th Airborne Regiment
o 331st Airborne Regiment (Kostroma)
o 1065th Artillery Regiment (Kostroma)
o 5th Air Defense Battalion
o 661st Engineering Battalion
o 674th Communications Battalion
o 15th Maintenance Battalion
o 1683rd Logistics Battalion

* 106th Airborne Division (Tula, Moscow Military District)

o 51st Airborne Regiment
o 137th Airborne Regiment (Ryazan)
o 1182nd Artillery Regiment (Naro-Fominsk, Moscow Oblast)
o 107th Air Defense Regiment (Naro-Fominsk, Moscow Oblast)
o 173rd Reconnaissance Company
o 388th Engineering Battalion (Plavsk, Tula Oblast)
o 731st Communications Battalion
o 1060th Logistics Battalion
o 43rd Repair Battalion, (Plavsk, Tula Oblast)

* 31st Airborne Brigade (Ulyanovsk, Volga-Urals Military District)
* 45th Special Forces Reconnaissance Regiment (Kubinka, Moscow Oblast)
* 38th Communications Regiment (Moscow Oblast)
In addition to these, according to various open sources, Russia currently has the following seven Spetsnaz Brigades:

* 2nd Independent Special Operations Brigade – Promezhitsy, Pskov Oblast;

* 3rd Guards Independent Special Operations Brigade – Roshinskiy, Samara Oblast;

* 10th (Mountain) Independent Special Operations Brigade – Molkino, Krasnodar Krai; activated July 1, 2003

* 14th Independent Special Operations Brigade – Ussuriysk, Primorsky Krai; 

* 16th Detached Special Operations Brigade – formerly Teplyi Stan, suburb of Moscow, now Chuchkovo.

* 22nd Guards Independent Special Operations Brigade – Kovalevka, Rostov Oblast

* 24th Independent Special Operations Brigade – Kyakhta.

Actually, there are more Spetsnaz units ranging from battalion size and smaller, but these are mostly specialized “officer only” units about which very little is known.