i dont mean to bag on you, but it doesnt seem like you know what autonomous replication is. i think if you have a clear understanding of what it does and how it works, you will see that pibond answered succinctly and accurately!
as for the mechanism, mechanisms of plasmid replication vary, from rolling circle to strand displacement to something called the "theta mechanism". feel free to peruse pubmed if you'd like to know more about each of these mechanisms
in terms of what rmm30 said i would agree. plasmids can sometimes integrate into the genome by recombination. however, once integrated they are no longer plasmids [read: plasmid = extrachromosomal dna] so although accurate, i dont think this is what the OP was asking for