Three separate applications have been made to the High Court, seeking to bring petitions to challenge the result of the referendum to repeal the Eighth Amendment.
Under the Referendum Act, applications to bring petitions to challenge the result must be presented seven days after the official result is published in Iris Oifigiúil.
The notice was published on 29 May and two applications were made at the High Court yesterday before the duty High Court judge.
A third application was made this afternoon.
All three have been adjourned until Monday when they will come before High Court President, Mr Justice Peter Kelly.
The first petition is being sought by Dublin woman Joanna Jordan who is representing herself. She previously failed in a petition seeking to overturn the result of the 2012 Children's Referendum.
Ms Jordan claims large numbers of potential no voters were unable to vote because of "de-registering". She also claims people who came home to vote were not questioned about the time they spent resident abroad and she claims there was an unexplained swing towards the Yes side.
The second application was made by Charles Byrne, a musician and piano teacher from Drogheda. He has made a number of claims about the Referendum Commission's information and booklet.
He says they failed to convey the nature, breadth and legal effect of the proposal to repeal the Eighth Amendment. He also claims "misstatements" were made by the Taoiseach and the Minister for Health during the campaign.
The third application was made by Ciaran Tracey, a retired civil servant from Leitrim. He also challenges the Referendum Commission's information campaign.
He says there was a serious omission in the booklet because it did not refer to a decision of the European Court of Human rights relating to the circumstances surrounding abortion in Ireland for fatal foetal abnormalities.
He also says the natural sincere sympathies of Irish people for women experiencing such pregnancies were played on by politicians advocating a Yes vote.
In her sworn document, grounding her application, Ms Jordan claims there was evidence of large numbers of potential no voters who were unable to vote due to de-registering.
She claimed these consisted of groups such as convents of nuns and residents of nursing homes.
Ms Jordan also claimed thousands of young Irish citizens "who were paid to return to vote", were not questioned at polling stations about the time they had spent resident abroad.
Ms Jordan further claimed that the tally of the number of votes cast per box, was "not always given" when requested by the No side, when voting closed on 25 May.
She said this begged the question as to whether the number of ballots counted from 9am on 26 May was the same as the number of ballots in the boxes at 10pm on 25 May.
Ms Jordan said she canvassed for a No vote for more than 17 weeks in Dublin city centre. She said initially the majority of people were in favour of a yes vote, but she said by the beginning of May there was a shift to the no vote, which continued until 24 May.
She claimed "a foreign journalist" told her on the eve of the referendum that the polls were showing a "2.6 differential" but within 24 hours, the result showed an increase of 20%.
She said such a swing was not possible.
Mr Byrne claimed various public statements by the Taoiseach and other Government members to the effect that the Eighth Amendment endangered women's lives, misled any voter who heard them and would have undermined the credibility of No campaigners making contrary assertions.
He also claimed he had been informed of "multiple instances" of people previously on the register who found themselves unable to vote because they were "without explanation" no longer on it.
He said examples were the Poor Clare communities in Galway and Clare.
Mr Byrne also claimed some of the people who returned to Ireland to vote and admitted to doing so illegally.
Mr Tracey told the court that the scope of the change to be put in place by repealing the Eighth Amendment had not been sufficiently addressed by the Referendum Commission.