Jeremiah Kirkwood, 43, and his sons Christopher, 23, and Wayne, 20, who are all from Island Street, appeared in the dock of Belfast Crown Court on Tuesday.
All three originally faced a total of 15 charges, but after pleading guilty to three charges each, the remaining counts were left on the books.
Each of the three men admitted to causing unnecessary suffering to four terrier cross puppies on dates between 1 November and 28 November, 2011.
They also pleaded guilty to possession of items for use in connection with an animal fight, namely a CD7 battery pack, handheld lamps, a green dog harness and an animal trap.
The trio also admitted a charge of keeping or training animals for a animal fight on dates between 10 July and 28 November, 2011.
The final charge relates to four bull lurcher dogs.
A co-accused, Jamie Edward Morrow, 19 and from McAllister Court in Belfast, originally faced three charges.
Two of these were left on the books after he admitted a charge of keeping or training an animal for a fight, namely a whippet cross Staffordshire bull terrier, on 27 November.
After the guilty pleas were entered, Judge Donna McColgan ordered that pre-sentence reports be prepared for all four men.
The Judge agreed to release them on continued bail but said: "This is no indication of the likely outcome of the case," which will be heard before the same court on 21 February, 2014.
Also appearing in the dock of the same court was Catherine Kirkwood, from Island Street in Belfast, who is the wife of Jeremiah and mother of Wayne and Christopher.
The 43-year old originally faced a total of 15 charges linked to animal cruelty and animal fighting.
A jury was sworn in to hear the case, but a prosecutor told the Judge and jury that the Crown would be offering no evidence against her.
Judge McColgan directed the jury to find Catherine Kirkwood not guilty of all the charges against her and when they were discharged, Kirkwood was told she was free to go.
Following Tuesday's court case, Detective Inspector Peter Mullan issued a statement, which read: "The corresponding police investigation has taken over two years and a significant amount of time and energy has been invested in bringing these individuals before the court.
"A partnership approach has been key to this process and I would like to thank the Ulster Society for the Prevention of Cruelty to Animals (USPCA), the Scottish SPCA, the Dublin Society for Prevention of Cruelty to Animals and members of the local community for their support."
DI Mullan added: "Police will continue to follow up all reports of animal cruelty linked to fighting offences, and when we are made aware of a possible breach in the Wildlife (NI) Order 1985 or Welfare of Animals Act (NI) 2011 for fighting offences, an investigating officer is assigned to carry out enquiries."
Offences against animals, such as domestic pets, should be reported to the animal welfare officer in local councils. Any suspected organised fighting offences should be reported to police on 0845 600 8000.
Any concerns or information in relation to animal cruelty on farm animals should be reported to the DARD.