Andrew Ball, 27, has already pleaded guilty to a string of charges relating to a crime spree through the city's northern suburbs in late February.

During the spree, Ball stole a car containing the baby.

That prompted a huge police search, employing large amounts of resources, including a police helicopter, and shutting down routes out of Canberra.

The baby was later found safe and well on a porch in Palmerston.

Prosecutors had charged Ball with an offence that related to the taking of a child for the purpose of gaining property.

Ball was fighting that charge, pleading not guilty to it late last month.

But the prosecution told the court on Wednesday that it had no evidence to offer on the charge, and asked that it be withdrawn.

Ball is still facing sentencing for 14 other charges, including abandoning the baby, which he has already pleaded guilty.

Other charges relate to a knife-point robbery of a pharmacy, and stealing cigarettes, a bottle of vodka, beer, a computer, a media player, a wallet, a Visa card, and a Ford Territory, all on the same day.

He is also facing sentencing for breaking into a Palmerston home.

Ball has not yet been committed to the ACT Supreme Court for sentencing.

The court has delayed the committal to allow for new laws to come into effect that let minor offences travel with more serious and related crimes to the higher court.

The case will come back before the ACT Magistrates Court next month.