The High Court is to hear three separate applications from people seeking permission to bring legal challenges to the result of the referendum on the Eighth Amendment.
The applications seeking leave to bring judicial review proceedings will be heard on 26 June.
Among the reasons cited by one challenger are allegations that student voters were not properly registered, concerns about tallies, balance in RTÉ's coverage, the Referendum Commission's information campaign and booklet and statements by the Taoiseach and the Minister for Health during the campaign.
Another has claimed large numbers of No voters were unable to vote due to "de-registering" and that thousands of young people "were paid to return home" to vote and were not questioned at polling stations about their residency abroad.
A petition can only be brought if the court considers the applicant has provided prima facie evidence the issues being complained about materially affected the 25 May referendum result.
The petitions are by Charles Byrne, a musician, of College Rise, Drogheda; Joanna Jordan, a homemaker, of Upper Glenageary Road, Dun Laoghaire; and Ciarán Tracey, a retired public servant, from Leitrim village.
Ms Jordan, who previously lost a challenge to the 2012 Children's Referendum, and Mr Byrne, are represented by lawyers while Mr Tracey is representing himself.
Mr Byrne, who has raised concerns whether a number of student voters at NUI Galway were properly registered, also wants to be provided with copies of the marked register of voters.
His counsel, Kenneth Fogarty SC, said his side had information from garda sources an estimated 600 students had queued daily at NUI Galway to be registered to vote and Mr Byrne believed a number of these were not properly registered.
Mr Fogarty said his side's concerns include registration of students "who should not have been registered on the criteria of eligibility"; tallies suggesting turnout of more than 100% in some cases and whether RTÉ's coverage of the referendum campaign was balanced.
Mr Byrne has also claimed the Referendum Commission's information campaign and booklet failed to convey the nature, breadth and legal effect of the proposal being voted on.
He further claims "misstatements" were publicly made by Taoiseach Leo Varadkar and Minister for Health Simon Harris during the referendum campaign.
Lawyers for the Sate said the Referendum Commission had no function concerning collation of information on the results of the referendum.
They said the State parties would consider Mr Byrne's request for the marked register but were concerned some of the grounds being advanced were "entirely nebulous".
Mr Tracey's case centres on the Referendum Commission's information campaign and booklet.
He claims it included a "serious" omission in not referring to a decision of the European Court of Human Rights in the case of D v Ireland concerning the circumstances surrounding abortion in Ireland for fatal foetal abnormalities.
That omission was sufficiently serious to have had a material effect on the outcome of the referendum, he claims.
Ms Jordan has made various claims, including that large numbers of potential No voters were unable to vote due to "de-registering" and of an unexplained swing towards the Yes side.
She also claims "thousands of young Irish citizens who were paid to return to vote" were not questioned at polling stations about their time of residency abroad.