The Roman grain laws were not and should not be thought of as a welfare system. They were, in origin, measures to ensure that famine did not occur in the city, whose population from an early date was artificially inflated by the ability to transport grain from areas (first from Italy--Campania and Apulia mostly--and later from the provinces) far from the immediate agricultural surroundings of the city. In some ways they resemble modern welfare programs, but their origin in earlier attempts to prevent famine in the city and the fact that supporters of grain laws argued that it was not largitio ("largess," the word means distribution of something for free) indicates that they're not really comparable

Grain laws went through a number of different forms, beginning with Gaius Gracchus' lex Sempronia in 123, which placed a regulation on the price of grain. All Roman citizens (not just the poor) could purchase grain at around 6 asses per modius. That the law applied to all citizens is important--obviously the reduced price benefited the urban poor much more greatly than landholders, as it was supposed to, but its application to all citizens is indicative of the role of grain laws in preserving the grain supply in general and preventing famine, not in supporting the poor specifically. A number of battles over grain laws were fought in the next few decades, but the most important change was the lex Clodia in 58 that abolished the cost set in the lex Sempronia altogether--how this was distributed, though, is unclear.

Now, understand that grain shortage in the ancient city is not analogous to food shortage for the poor in modern society. The vast majority of urban inhabitants at late Republican Rome were day laborers living in shabby one-room lightless tenements that, apart from catching fire all the time, collapsed due to shoddy building measures, like walls made of rubble. Disease was rampant, partly due to horrible living conditions among much of the city but also because of constant immigration. Immigration into the city is significant, because the city had, as Ian Harrison puts it, "an essentially fluid population." Mortality from disease and starvation within the Republican city was probably high enough that residents were constantly being replaced by people coming into the city from Italy and the provinces, and besides that thousands of people entered and left the city annually searching for seasonal work in building projects and the like--these people also wandered around within the city after entering, since the high cost of living in the city and the necessity to chase daily work must have prevented permanent shelter for a lot of people, who probably often paid their rents daily. The meager wages of the day-workers that made up so much of the population of the city were only barely sufficient to pay a single person's rent and keep him clothed and fed. If we take 3 denarii a day as the "average" day's wage in the city (based on Cicero's statement--there's a lot of problems with assuming this is a real average though) then even Gaius Gracchus' 6 1/3 asses per modius is a not insignificant chunk of a worker's daily wage, and higher grain prices were crippling. Nor was the amount really enough--a single modius, or the alternate 5 modii per month, was not enough to keep a person's family fed, although it might keep him himself out of starvation (in the words of my thesis director, the distributions of the lex Clodia "were nice, but they weren't going to feed your family"). So even with grain distributions the urban poor might have to purchase grain on the market, and state-subsidized grain might not be available in high enough quantities to allow individuals to repeatedly purchase. Even fairly small fluctuations in the price of grain could therefore have horrifying effects, and shortage was even worse--the success of the lex Clodia was plagued in its early years by a critical shortage of supply, leading to Pompey's appointment as curator annonae and the grant to him of 40 million sesterces to purchase grain and fix the supply to the city. The possibility of famine was not restricted to a relatively small portion of the population unable to afford food, as in modern welfare--the modern economy and modern methods of food production have fundamentally changed the way that we obtain food. Pompey in his cura annonae tried to limit the recipients of free grain and compiled a list--which contained 320,000 members, fully a third of the city's population, and only adult males could be on the list!

The lex Clodia and Pompey's cura annonae encountered problems of abuse by the wealthy as well. Cassius Dio reports that many masters freed their slaves to have them collect free grain, some of which would then be provided back to the former master as part of the services owed a former master by a freedman. This abuse was part of the reason for Pompey's establishment of a list of recipients, but nothing was actually done to stop the practice, only to get an idea of how many people were doing it--after all, since Gaius Gracchus' time these distributions were theoretically supposed to be for all citizens. Caesar managed to get it down to 150,000 (!) but that was only accomplished by promising that the praetors would promptly and automatically enroll new recipients whenever one died and by settling tens of thousands of the urban poor in colonies--Caesar also appointed two extra aediles to oversee supply and prevent another shortage.

Augustan grain laws, however, are probably what you're referring to when you speak of the grain distributions as being welfare. Augustus' cura annonae set the standard for grain distribution and prices within the city throughout the Principate, with only minor changes in later years, although Augustus' lex Julia de annona, which set legal penalties for the obstruction of the grain supply (in the Republic sellers often artificially created scarcity to drive prices up), was to be added to by later legislation of other emperors (notably Claudius). Under Augustus the recipients were eventually stabilized to 200,000 (although they fluctuated until then, once going back up to 320,000). But don't mistake this for a program intended to search out the poorest Romans and provide them with food. The Augustan grain program was, to quote the New Pauly, "not a social measure but gratuities for a privileged social group." Recipients of Augustan grain received special tickets (tesserae) which could be traded and even passed on as an inheritance. They were thus what the OCD calls a "privileged minority." No longer could those not on the lists, as under Caesar, be assured of having a chance of being automatically enrolled when a member died--since tickets could be inherited if you were on the list you were on it for the long run, even if your grandson came to own all the land from Antium to Minturnae. And since tickets could be sold there was no guarantee that a recipient hadn't just bought his ticket from some poor stupid asshole who sold it to him for...whatever reason. Even from the beginning we can't know if the tickets went only to the poorest citizens, who would have been rather difficult to track down and died at a horrifying rate--probably some attempt was made, but we're not told of any, and it would've been a real pain in the ass to find the 200,000 poorest citizens. And again, the grain distributions still weren't enough to supply a family, necessitating the further purchase of grain--Augustus' most important contributions to the food supply of the city was the establishment of a regular grain supply with regulated prices and shipments, which largely (though far from entirely) cut out the danger of sudden famine or price fluctuation, not the distribution of free grain