Counties and Sheriffs
Counties/ Shires I
The Anglo-Norman lordship sought to replicate shire government by royal sheriffs through Ireland. The organization of shires spread slowly. Dublin was the first shire established at the end of the 12th century. Waterford and Cork had commenced to be organized at about the same time.
By the early 13th century, Waterford with Cork and Munster, Limerick, Tipperary and Thomand were the  main shires which seem to have been established. At that time Ulster with Ureal (Louth) and Meath had been entrusted to seneschal or stewards who were not yet described as sheriffs.
Kerry was established as a separate shire in the 1230s. By the middle of the 13th century, Munster appears to have been broken up and Limerick and Tipperary became separate units.
By the same time Connaught was a shire. The Sheriff of Roscommon appeared at the end of the 13th century. At that stage there were nine shires, Dublin, Waterford, Cork, Kerry, Louth, Limerick, Tipperary, Connaught and Roscommon. Two further were added shortly afterwards.
Counties/ Shires II
Dublin consisted of the present county of Dublin together with substantial parts of Wicklow and half of the former liberty of Meath. The sheriff of Dublin exercised jurisdiction over the cross-lands i.e., lands held by the church directly from the crown exempted from liberty jurisdiction within the four liberties of Leinster, and the liberties of Trim and Ulster. If the seneschals of these liberties failed to exercise the writ, the Dublin sheriff was entitled to enter and execute it.
Legislation at the end of the  13th century mentioned made Meath a separate shire with its own sheriff and county court. It made Kildare and its cross-lands a separate shire and removed the jurisdiction of the Dublin sheriff. Kildare had been organized as a shire even when it was a liberty.
Wexford, Kilkenny and Trim were liberties. However, in a liberty, the sheriff and seneschal took an oath  to the King and the lords.  But at the end of the 13th century, the liberty of Ulster was held by the King and at various times during the 13th century was governed by his officials.
Within shires in England, the territories were divided into cantreds. This had elements of the old Gaelic division of ceads . Some followed the old Gaelic units, but most did not.
It appears that each cantred had its courts, which  were held by a sheriff. It appears they were held monthly on a particular day of the week generally in the principal town of the shire.
Other Units
The northwestern part of Ireland was altogether outside the shire or liberty system. There were also other enclaves of territory still held by native Irish.
The cross-lands which were church lands were outside the jurisdiction of the liberty but were attached to the nearest shire for administrative purposes. Not all church lands were necessarily cross-lands.
Some liberties reserved the right of the Kings and effectively formed enclaves in which a greater degree of administration remained. The terms of the grants were determinative.The charters determined the extent of the monks or clergy’s rights.
Sheriffs
Sheriffs were appointed in a number of different manners. Some were appointed directly by the  English Crown. Others were appointed by the Justiciar. By the late 13th century, the sheriffs and the bailiffs who answered to the exchequer were to be appointed by the treasurer and barons of the exchequer and removed by them only.
The sheriffs performed a variety of functions. They  raised various revenues including customary revenues and fines. The revenues of certain counties were significant.
Most of the revenues collected by the sheriff derived from activities of the central government. Under the order of the exchequer, the sheriff was responsible for collection of amercements imposed by the royal courts, fines for having the King’s grace, fees for chancery writs and other items of the crown’s revenue. He collected scutages of lower tenace and other local subsidies and charges.
Sheriffs and Administration of Justice
The sheriff exercised functions as an officer of the central court. He organized assizes of the judges. He convened juries. He organized and convened the court generally. He summons the shire to bring pleas and those who wished to complain. Writs were generally served by his sergeant.
The sheriff levied debts recovered by judgment, one of the sole remaining functions of the office. Judgments were enforced by ceasing and selling goods. A sheriff could be amerced (fined) for failure in the performance of his functions.  The sheriff was responsible for the custody of prisoners well before trial and until they provided security for payments of amercements.
The sheriff had military and police functions. Most sheriffs were ordered to keep armed forces given that border warfare pertained in most shires.
When attempting to arrest persons who had been indicted it might be necessary to call a posse. This may be required for levying debts. He might commission, intervene, to prevent a breach of the peace.
Judicial Functions of Sheriffs
The sheriff had his own judicial functions in the county court where he was president and responsible for the conduct of business. Judicial functions included appeals of felony and with a range of civil matters.
The administrative functions of this county court become more important than judicial functions by the end of the 13th century. Various knights of the shire and coroners were elected, and they began to form a local assembly.
The sheriff exercised greatest judicial power in his tourn. He dealt with minor offences directly reserving pleas of the crown for the royal justices. The sheriff exercised functions within liberties and  decided which matters were those for liberty courts, church courts or royal courts. There were a wide range of other offences which was under his jurisdiction.
The sheriff was to enquire into wardship marriage and escheat. These covered a range of administrative civil and criminal matters. He enquired in relation to criminal matters, burials, obstruction of the highway, waterways and a variety of other matters.
Administrative Functions of Sheriff
The sheriff had substantial administrative duties. These included the repair of castles, jails and the expenses of certain royal officials and administrators. The sheriff was responsible for the construction and maintenance of a variety of public works.  The sheriff made returns and payments to the treasury who accounted for them.
Sheriff had administrative duties, some in conjunction with the coroner. He arranged for the election of coroners and required them to undertake office.
He was responsible for the organization of election of knights of the shire and they were summoned to  parliament. He proclaimed statutes in market towns and fairs and in county courts. Where persons were under duties to repair bridges,  causeways and things obstructing navigation, he was entitled to require them to fulfill their duties.
The sheriff was assisted by a range of staff in his various duties. He could appoint sub-sheriffs to act in his absence. They were obliged to give surety for the due performance of their functions. He could appoint clerks responsible for records in judicial and administrative matters. He could appoint receivers to collect taxes and similar levies.
Sergeants
There was a body of sergeant’s equivalent to the English hundred bailiffs who were ostensibly under the control of the sheriff.  In most counties, there was a hereditary chief sergeant who held office from the King and was not under the control of the sheriff. He could be removed for misconduct by the Justiciar or justices. Some were notionally at least under the control of the sheriff.
The chief sergeant often exercised his office through a deputy. Under the chief sergeants, there were sergeants of cantreds who he appointed and they in turn appointed sub-sergeants.  The office of sergeants might be profitable, and sums were paid by sergeants for the office in some cases. The sergeancies earned a revenue.
Many routines functions of the sheriff were performed by the sergeants of the county so that there was a likelihood of bribery and extortion. Many sergeants were found guilty of offences.
The sergeant had financial responsibility to those he appointed in office. He could be liable for amercements if they were unable to pay. He might be subject to amercements if prisoners escaped from custody. He might ultimately forfeit his office for failure to perform his duty to the satisfaction of the Justiciar.
The chief sergeant was generally a substantial landowner. The sub-sergeants were of lower social rank. Chief Sergeants had frequently inherited their offices.
Other Officers
Coroners were universal. The Coroner was elected by in the county court. Often, it was an unpopular office and persons had to be constrained in some cases to accept it. The coroner was concerned with pleas of the crown, and in particular violent deaths. He was responsible for taking the goods of persons indicted in inquisitions. He relied on the Sheriff in relation to arrests. He deputized for the sheriff in some instances.
Keepers of the peace had a quasi-military function. There were several in each cantred at certain periods. Some shires appointed escheators and deputies.
Emissaries of the central government accompanied local officials. They include exchequer officials  seeking to collect crown debts, clerks of the markets, investigators of weights and measures and escheators.