" Leath Cuinn (Conn's Half) and Leath Moga (Mugh's half) are legendary ancient divisions of Ireland. Leath Cuinn was the island north of the Esker Riada (east-west drumlin belt from Dublin to Galway Bay). Conn Cétchathach, for whom this division is named, was a retrospective ancestor of the Connachta and Uí Néill dynasties. Ireland's legendary ancient division into Leath Cuinn (Conn's Half) and Leath Moga (Mugh's half) resulted from the battle of Maigh Nuadad in 123 A.D. Conn, defeated by Eoghan Mor (also known as Mug Nuadat), was forced to accede to the division of Ireland into two halves: The North - taking in Connacht, Ulster and Meath - would be Conn's Half; The South - taking in Munster, Osraighe and Leinster - would be Eoghan's Half. In the twelfth century, the north-south division of Ireland was used as a basis for the new division of dioceses in Ireland at the Synod of Ráth Breasail." From: DBpedia
The descendants of Conn Cétchathach or Conn of the Hundred Battles occupy the largest area of DNA M222 concentration in their land of Donegal and Tyrone, Ireland and there may be a germ of truth in the old legend. Almost all La Tène objects are found in Conn's Half (see the top three images below), and some of the most important Irish artifacts such as Ogham script and hill-forts are almost all found in Eoghan's Half (see the bottom three).
Prof. J.P. Mallory in his book "The Origins of the Irish" write about this and is quoted below. (Four of the images are his.)
After 600 BC and before the start of the La Tène in Ireland about 300 BC there seemed to be a profoundly obscure Dark Age, at least in terms of settlements and artifacts, and when the curtain rose again during the La Tène, the overwhelming majority of metallic remains were confined to the northern two-thirds of the island, with Munster traditionally appearing as either poorly settled or a backwater of the rest of Ireland. It now seems probable that a new technology of ironworking spread across Ireland at about the same time that it penetrated Britain, so contacts between the two islands were clearly still taking place. The authors of the report to the Heritage Council indicated that they believed that the period around 700 BC (the beginning of their Early Iron Age) marked one of the two significant transitions witnessed during the Iron Age. There is also some evidence of continuity between the earlier Hallstatt period and the following La Tène that can be seen in the largest of the Iron Age sites, the ancient royal sites of Ireland.
The early medieval Irish believed they could access their pagan past through a series of tales centred largely on the exploits of the prehistoric Ulstermen and their less than friendly relationships with their neighbours in the other provinces, especially Connacht. The major set piece of tales, known as the Ulster Cycle, was the Táin, the great cattle raid that included a series of duels between Ulster's champion CúChulainn and the warriors of Queen Medb. The stories are set in a series of ancient provincial capitals such as Emain Macha in Ulster and Cruachain in Connacht, which are archaeologically identified respectively with Navan Fort (Emain Macha), outside Armagh, and Rathcroghan, near Tulsk, Co. Roscommon. Other 'royal' sites are Dún Ailinne (Knockaulin, Co. Kildare), the ancient seat of the kings of Leinster; Cashel, the royal site of Munster in Co. Tipperary; and Tara, the legendary capital of the (equally legendary) High King of Ireland. To these one might add the more overtly ceremonial site of Uisneach, Co. Westmeath, the ritual 'centre' of Ireland. Most of these sites have seen either excavation or surveys, and they all exhibit features that indicate they were important Iron Age centres. From the perspective of the Irish of the early Middle Ages who, as we will see in the next chapter, imagined themselves as the last of a very long series of invaders, these Iron Age sites were very much part of their own ancestry and not the ruins of remote and ancient peoples. While earlier races of heroes or gods might be confined to much earlier megalithic tombs, the Iron Age centres are the earliest monuments that the Irish attributed to themselves and, indeed, they may have deliberately associated themselves with these sites in later historic times in order to emphasize claims of legitimacy. For this reason it is important that we understand these sites.
Although the centres are far from identical, some share a number of important common features. Navan, Knockaulin and Tara, for example, all present their ceremonial centre in a henge-like enclosure. Unlike the Late Bronze Age hillforts that, as one would expect of a defensive structure, had their ditches outside their earthen, timber or stone ramparts, these Iron Age enclosures reverse the relationship. The henge was a relict of the distant past, the type of ceremonial enclosure that was widespread in both Britain and Ireland c. 3000 BC. Where dating evidence is available, it suggests that these Iron Age enclosures, measuring anywhere from c. 285 to 500 m across, were built c. 100 BC. The main ritual site at Rathcroghan was also surrounded by a ditch, although there is no trace of what side its bank lay on.
The interior of the enclosures was not, so far as we can tell, densely filled with houses. Rather, at least in two of them, we find an early phase of figure-of-eight structures. These consist of a smaller round structure attached to a larger enclosed 'courtyard' that was approached by a funnel-shaped walkway. Both Knockaulin and Navan replaced the earlier figure-of-eight structures with very large circular structures, built of concentric rings of upright timber posts, measuring 40 m or more in diameter. At their centre was a post (Navan) or tower (Knockaulin). At the Rath of the Synods at Tara there are two adjacent enclosures that were perhaps comparable to the figure-of-eight structures and, as at the other sites, these were subsequently replaced by a larger multi-ringed structure. A recent survey of Rathcroghan mound has revealed the presence of a 32-m circular structure. Finally, three of the sites also possess sizeable mounds. The enclosure at Tara, the Ráith na Ríg, surrounds an earlier Neolithic passage tomb (the Mound of the Hostages)37 that later featured as a cemetery for Early Bronze Age burials. At Navan the mound covers both an earlier figure-of-eight and the 40-m structure, while the circular structure at Rathcroghan is also encased within its mound. To these we might add a very low (0.8-m) mound at Knockaulin. At Navan there appears to have been a well-ordered sequence of events in which the earlier 40-m ceremonial structure was first filled with limestone cobbles, then its timber outer structure was set on fire, and finally sods were placed on it to form a mound. Such behaviour has sparked no end of archaeological speculation, but one potential explanation is that the occupants of Navan were copying those at Tara and felt the need to erect their own mound that might have provided a ritual access to the Otherworld.