My understanding is different to Karl’s. I was always under the impression that to be a HMO each tenant/room needed to have a separate tenancy agreement.
Karl is correct. Whether its individual tenancies or a joint tenancy is irrelevant to whether the property is an HMO. If 3 people live there that are not all related by blood or romantic involvement, then its an HMO and the full HMO Management Regulations 2006 apply. Where the local authority has implemented Additional Licensing for 3 person HMOs a licence will also be required.