Before 2010 there were three ways to consolidate authoritarianism (Putin knows it and did all three) - 1. built vertical of power, appointing governors and making them deliver votes as part of the political machine and eliminate checks and balances in the system 2. undermine independent wealth - imprison oligarchs, it is fairly easy given all the violations of 90s' privatizations and take their media resources, or, alternatively coopt them into power and 3. build a pro-presidential party that will unite elites under one person or idea and keep them in check, so that there are no political forces astray and there is no alternative organized political force in the country.
Some leaders did not do the third thing, preferring instead to jockey on elite disagreements and acting as independent above-clan arbiters (Kuchma, for example). They did not, therefore, explicity support any parties, nor did they stick themselves to any. Some of them are still around, some have been kicked out.
Some did this as an additional check against color revolutions and for the time being, it worked. The mechanism was explained quite simply by daughter of President Nazarbayev of Kazakhstan: to consolidate/form a party "with which no other party will be able to compete in the next 50 years." As it usually happens, the institutional innovation came from Russia and was quickly and effectively adopted in Kazakhstan (Nur Otan party) and even Kyrgyzstan (notorious Alga, Kyrgyzstan and then Ak Jol). Outside the CIS the model was also adopted - one example I am aware of is pro-presidential Constitutional Democratic Rally in Tunisia, though the party was founded long before Putin came to power.
But the signs coming are now that such pro-presidential parties are losing ground, as their functionaries "bring down" popularity of their founders by inertia (Russia, Kazakhstan) or vice versa (Tunisia). Putin long used United Russia to pursue his agenda and keep elites united, but now when UR is hated and termed "party of crooks and thieves" it should be hard for Putin to get rid of them and stay clean.
A natural reaction from autocrats might be to let the hated parties "sink" and get new faces to the new fake parties. Part of the game will involve creation of pseudo-opposition and this is what is going on now in Russia with the fake pro-business and rightist parties coming to the political arena. Maybe they are geniune in their opposition and pro-business attitudes, but the burden of proof and demonstration lies with those suspected of hidden complicity to Kremlin's agenda
p.s. when looking up something on Tunisia I saw this picture. If not for the appeal on the right, would have thought Ben Ali got much older and lost weight :)