ASR is consumed as a service, but requires some on-premises components.
ASR is consumed as a service and doesnt require installation of extra VMs in Azure (anymore). An on-premises management server virtual machine is required which includes the Process Server-, Configuration Server- and Master Target Server component. Configuration requirements of the management server VM depends on the number of VMs to be replicated. Extra process servers can be added, depending on the number of virtual machines and daily change rate of the replicated data.
Microsoft, Azure Site Recovery/Current, VMware to Azure