On rituals at crossroads: 

[...] “Crossroads are liminal points or transitional gaps between defined, bounded areas, that is, between roads or between the areas of land that the roads define.

These rituals can be divided into two categories, both of which reflect their liminality: 1) those in which an individual sought help and protection at an uncertain liminal point, and 2) those in which the detachment of the liminal point was exploited.”

On offerings at crossroads:

“Crossroads, precisely because they were unclaimed “nowheres,” were among the few appropriate places to leave material expelled from society. According to several sources, [...] the polluted remains of household rituals, were left at the crossroads.” 

On symbolic display of parricides:

[ parricide: the killing of a parent or a near relative; someone who committed parricide ]

[...] “that Plato only prescribes this purifying treatment at the crossroads for parricides -- the most polluted and polluting of murderers -- indicates that what is of concern is not the punishment of the murder per se (which, after all, already would have been accomplished by this point) but the expulsion of a particularly dangerous bloodguilt. [...] This alternative combined the ritualized expulsion of pollution to a liminal place with the practical removal of the offending corpse.”

On exploiting the magic at crossroads: 

“If one sought contact with the unquiet dead, then a crossroads was the place to look. It is possible, too, that only selected crossroads became burial places for atypical corpses and thus, repositories of restless ghosts. [...] perhaps, there were appointed crossroads for the burial of other stigmatized dead, chosen for their distance from the city or other qualifying circumstances.

By manipulating the souls who gathered at crossroads, the magician, in his own way, exploited the liminality of the crossroads that brought him there; he recalled the polluted souls that others had cast out.”