Final answer:
Dispersive replication leads to new duplex strands comprised of both old and new DNA fragments, with no continuous parental strand or duplex preserved.
Step-by-step explanation:
The type of replication that results in both old and new DNA within the new duplex strands, with neither the parental strands nor the parental duplex being preserved, is known as dispersive replication. This model suggests that after replication, each strand consists of interspersed segments of both parental and newly synthesized DNA, with no continuous old or new strand. This contrasts with semi-conservative replication, where each daughter DNA molecule contains one strand from the parental DNA and one new strand, and conservative replication, where the original DNA strands are preserved intact and the daughter molecule is entirely new.