Charles Vincent Read, 24, appeared on Tuesday in Hobart Magistrates Court and changed not guilty pleas originally entered in August relating to several charges.
Police had alleged Read evaded officers and failed to pull over while driving when disqualified at Bridgewater, north of Hobart, on February 15.
According to court documents, he was "careening" at speed in and out of lanes on a highway after all four tyres of his car were punctured.
Read was found with the drug methylamphetamine and two unregistered guns, a Norica .22 calibre rifle and 303 British Savage Arms Lee Enfield bolt action rifle.
He entered guilty pleas to charges including possessing a controlled drug, possessing unregistered firearms, evading police, driving while disqualified and possessing ammunition when not the holder of the appropriate licence.
He also pleaded guilty to stealing, unlawfully possessing a dangerous article in a public place as well as breaching bail and assaulting a police officer.
Read, who is in custody, will be assessed for eligibility for a drug diversion program and will return to court for sentencing at a later date.
Magistrate Chris Webster said Read could face prison time.
Read maintained a not guilty plea to a charge of aggravated assault and hasn't entered a plea to several related offences including aggravated burglary.
He had previously pleaded not guilty to dangerous driving, with the matter to be heard in the Supreme Court of Tasmania.
Mark "Chopper" Read died in 2013 and was the subject of a film in 2000 about his life and time in prison.
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