Allowing Barnaby Joyce to remain in parliament would reward ignorance and fuel the same chaos and uncertainty which has engulfed Australian politics this year, the High Court has heard.

Former solicitor-general Justin Gleeson, representing Mr Joyce's political nemesis Tony Windsor, delivered the blunt warning as he called for the deputy prime minister to be booted from federal parliament.

Mr Gleeson today argued the constitutional rules around dual citizenship were black and white, based solely on whether or not a political candidate was a citizen or subject of a foreign power.

Letting Mr Joyce and others off the hook on the basis they were unaware of their dual citizenships would set a dangerous precedent, he said.

The community would come to expect there may be any number of dual citizens sitting in federal parliament, he said

Embattled deputy prime minister Barnaby Joyce. (AAP)

This would create an environment where the media, political opponents and the public went searching for people with potential dual citizenship problems and tried to squeeze information out of them.

"We will then have a sequence, like we have seen this year, of people in the parliament sitting there with this uncertainty hanging over their status," Mr Gleeson said.

He argued that Mr Joyce did not follow the "ordinary" way to overcome issues of dual allegiance and renounce his status as a New Zealand citizen - or even attempt to - before he sought to stand for election.

New Zealand laws conferring citizenship on Mr Joyce could not be considered exorbitant, and he could readily have severed his trans-Tasman links without onerous conditions, Mr Gleeson argued.

Tony Windsor hopes to challenge Mr Joyce again in the seat of New England. (AAP)

The barrister for former Nationals minister Matt Canavan also delivered a stark warning to the High Court today.

David Bennett QC said disqualifying people born in Australia from federal parliament on the basis they were foreign citizens by descent could lead to "genealogical witch hunts" at every election.

Mr Bennett said there would always be some whose desire it was to remove politicians from parliament.

"If one allows citizenship to be passed by indefinite succession, one is going to have such people engaging in genealogical witch hunts which will occupy this court every time there is an election," he said.

He argued it would be totally inappropriate and offensive in a "nation of immigrants" to apply that to the part of the constitution that bans dual citizens from standing for election.

Mr Bennett said there was still doubt as to whether Senator Canavan was actually an Italian citizen and that not even a royal commission with unlimited time and resources would be able to work it out given the "quirks" of Italian law.

However, Mr Gleeson later argued a person's status as a foreign citizen disqualified them, regardless of whether they knew about it or not.

The full bench, sitting as the Court of Disputed Returns, also heard from lawyers representing former Greens senators Scott Ludlum and Larissa Waters, as well crossbencher Nick Xenophon.

The hearing continues tomorrow, where the court is expected to hear from lawyers for One Nation senator Malcolm Roberts.