Helicopter money started as an abstract thought experiment: money would be created and just distributed to individuals by helicopter. If we think of a consolidated government which includes its central bank, then it is clear that in technical terms this is a combination of monetary policy (the creation of money) and fiscal policy (the government giving individuals money). Economists call such combinations a money financed fiscal stimulus. With the advent of Quantitative Easing (QE), it has also been called QE for the people.
Some have tried to suggest that central banks could undertake helicopter money for the first time without the involvement of governments. This is a fantasy that those who dislike the idea of government have concocted. Others who dislike the idea of fiscal policy have suggested that helicopter money is not really a fiscal transfer. That is also nonsense.
Helicopter money is a particular form of money financed fiscal stimulus. It has two key features among the class of all possible money financed fiscal measures. The first is that it involves a particular kind of fiscal policy. A helicopter would distribute this fiscal transfer randomly, but what most people have in mind is an equal distribution to every person (adult?) - a kind of reverse poll tax, or what economists would call a lump sum transfer. The second is that, once the apparatus for helicopter money had been established by the government, its use would be initiated by the central bank, whereas other fiscal transfers are initiated by the government.
I want to suggest that it is this second aspect that is critical. You could imagine the government making a transfer to every person, and you could also imagine the central bank distributing money to only those people who paid income tax the previous year. The fact that helicopter money is initiated by the central bank seems more like a defining characteristic. If helicopter money could be ordered by the government, we would say that the central bank was no longer independent.
This defining feature of helicopter money is also what makes it attractive from the point of view of macroeconomic stabilisation. It removes the Achilles’ heel of the consensus assignment. The consensus assignment allocates demand stabilisation entirely to monetary policy run by independent central banks, while fiscal policy’s role at the aggregate level is to focus on deficits and debt. The Achilles’ heel is that interest rates can no longer be used to control demand when they hit their lower bound. QE tries to fill that gap, but helicopter money would be much more reliable and effective. Of course governments could make the transfers themselves through deficit finance , but the evidence of the last few years is overwhelmingly that they become fixated with reducing deficits in a deep recession with the result that we get fiscal contraction rather than stimulus.
This last point raises a potential problem with helicopter money, which is that government may take the opportunity to offset its impact by raising taxes or reducing transfers, and we end up simply monetising part of government debt. One would hope that does not happen for three related reasons: first, governments are rather less agile than central banks, second, good governments should be working with fiscal rules that specify a medium term plan for deficits, and third the monetary stimulus is only temporary, so there would be little long term benefit in terms of deficit reduction if governments tried to play this game. 
If initiation by the central bank is the defining feature of helicopter money, and this policy always requires the cooperation of government, might it be possible to imagine a form of helicopter money that was more ‘democratic’? Why could the central bank not give the government the money, on condition that it was used to increase transfers or reduce taxes in some way? A left wing government might decide that, rather than giving money to everyone including the rich, it would be better to increase transfers to the poor. A right wing government might decide it should only go to ‘hard working families’, and turn it into a tax break. We could call this democratic helicopter money.
I can see two problems with democratic helicopter money. Suppose the government decided to use the money for a tax break that went to people with a very low marginal propensity to consume. If the central bank fixes the scale of the monetary stimulus beforehand, it makes that stimulus much less effective. If it increases the size of the stimulus following the government’s decision on how to spend it, this gives perverse incentives to government: think of inefficient ways to stimulate the economy, and we will give you more money.
One way to reduce such problems is for the central bank and government to cooperate over the size and form of any money financed fiscal stimulus. This could have added benefits. Most studies, and theory, suggest that the most effective fiscal stimulus tool is to bring forward public investment projects. With democratic helicopter money, the central bank and government could cooperate on this policy, rather than or as well as implementing a tax cut or transfer. However such cooperation creates a second potential problem, which is that it puts at risk the perception (and perhaps the reality) that the central bank was both independent and non-political.
Given these problems, why even think about democratic helicopter money? One reason may be political. A long time ago I proposed giving the central bank limited powers to make temporary changes to a small set of predefined tax rates, and I found myself defending that idea in front of the UK’s Treasury Select Committee. To say that the MPs were none too keen on my idea would be an understatement. Making helicopter money democratic may be what has to happen to get politicians to support the idea.
 Combined with QE, this could become a money financed fiscal stimulus. An alternative way of avoiding this deficit fixation is to get governments to adopt a fiscal rule where, when interest rates were likely to hit the lower bound, the central bank in cooperation with the fiscal council proposes increasing the deficit by adopting a fiscal stimulus package of a particular size. This is the proposal in Portes and Wren-Lewis (2014). If instead the stimulus package was money financed, it becomes helicopter money.
 None of these considerations, even collectively, rule out the possibility that governments could negate helicopter money in this way. This point and the previous footnote show that all we are really talking about here is the effectiveness of different institutional mechanisms of persuading governments to allow fiscal stimulus in a recession, and to avoid the adoption of austerity.