More parents are taking their children to the GP than expected under the new under-13 scheme.
The influx - up to 20% more than expected - raises questions about whether the Government has allocated enough funding.
Funding is set at two visits per child per year - but in at least one case that has already been exceeded since the scheme started more than two weeks ago.
The Government has provided funding for children under 13 to attend the GP free of charge.
WellSouth Primary Health Network chief executive Ian Macara said early data suggested the uptake was up to 20% more than expected.
He agreed it might be a causing concern for some practices, whose participation was optional.
''We haven't had our data confirmed, but from what we've seen so far, it looks like a higher uptake than what it was for the under-6s.''
It might be relieving pressure on public hospital emergency departments, which would be positive, he said.
The scheme, which started on July 1, would be reviewed after three months.
Practices were able to pull out every quarter: ''We would encourage them to speak to us first and see if we could get a solution''.
Mr Macara is pleased with how many have signed up in the South - all but a handful of 85 practices.
Amity Health Centre partner Dr Susie Lawless had noticed the high demand for the scheme.
''Anecdotally, we are seeing families bringing their kids back more freely and more lightly.''
She was pleased, because it meant people were accessing health care. But it raised questions about the funding cap of two visits.
One family brought their child to the clinic three times since the scheme started, ''which they would not have done had there not been free care''.
''It's absolutely fine, because they should be coming in.
''The problem is that there isn't, as far as I know, any mechanism built into the funding formula to correct for that,'' Dr Lawless said.
