Protein covalently bound to the viral DNA that acts as a primer for viral genomic replication by DNA strand displacement. Assembles on the viral origin of replication in an initiation complex with viral polymerase, DBP, host NFIA and host POU2F1/OCT1. During initiation, the polymerase covalently couples the first dCTP with Ser-580 of pTP. The terminal protein stimulates the template activity over 20 fold compared to protein-free templates. Neo-synthesized viral genomes are linked to two preterminal proteins, one for each 5' end. These new genomes are encapsidated in the nucleus, and during capsid maturation by viral protease, preterminal protein is first cleaved into intermediary (iTP), then into mature TP. May play a role in host nuclear matrix localization of genomic DNA. Heterodimer with the polymerase; this heterodimer binds to bp 9 to 18 of the genome. Interacts with host POU2F1; POU2F1 binds to the auxiliary sequences in the inverted terminal repeats and tethers the pTP-POL heterodimer to the origin DNA thereby participating in the assembly of the pre-initiation complex (POL-TP-DBP-NFIA-POU2F1). Preterminal protein is used to replicate viral genome, upon genomic encapsidation it is processed first into iTP and finally into TP by adenovirus protease. Belongs to the adenoviridae terminal protein family.