All current life having a common ancestor does not imply that life only rose once. It implies that of the many times life may have arisen, the descendants of only one of those life forms survived to the present. Most biologists find this credible due to the "compound interest" argument.(and please don't ask me to give the names of all those biologists in the 'most' category).
The compound interest argument is as follows: suppose that there are one trillion primitive forms that have arisen independently and have about the same generation rate. We'll suppose that in some typical generation time they replicate on the average by a factor of 1.005. That is, about one half of one percent of them duplicate in this time. Suppose that one of those trillion forms undergoes a beneficial mutation that allows it to reproduce at the rate of 1.0051, i. e., just slightly faster than the rest of the entities. At the time of its beneficial mutation, it represents just one trillionth of the total biomass. After 1000 replications, the descendants of the mutated form will still only represent slightly more than one trillionth of the total biomass. But after one million generation times, the mutant's descendant's biomass will be 1.6x10^31 times as great as the non-mutated forms. That is, there will be 16 million trillion trillion times as many of the mutants as non- mutants. All but a very miniscule part of life will have descended from this one common ancestor. If a million generations sounds like a lot, remember that that is about the number of generations your gut bacteria will go through during your lifetime.
Of course, this is a very simplified example that assumes that all these primitive life forms grow independently. In actuality, they will be competing for the same limited resources, holding up their tiny bowls and begging 'more'. As the mutes begin to swamp the non-mutes, they will consume all the goodies, and the non-mutes will die out. Life's a bitch. So, few biologists doubt that various forms of pre-life arise independently, or that they might still arise on occasion. But this is a race that swiftly went to the swiftest.
I'll write out the simple formula used in the preceding, but I have no idea how it will appear in the post on your computer:
F = ((1.0051)^N)/((10^12)x(1.005)^N)
where F is the fraction of mutes after N generations (or the fraction of the biomass they represent). If you use this and put in N = 10^6 (one million) into your calculator you will just get an overflow error. But this formula is identical to:
F = ((1.0051/1.005)^N)/(10^12)
which should work fine on any scientific calculator.
It is this kind of argument that allows one to believe that life can arise very easily and commonly, and yet lead to a single descendant family as we now observe. There are many books on the various theories of abiogenesis, some of them actually very good, and a couple of journals devoted to the subject. If you like, I could post an short annotated bibliography of the ones I've read, but your best bet would be to go to Amazon.com and look up 'origin of life'. Read the customer's comments for a lot of insights and laughs. Unfortunately, the best book: 'The creation of life : past, future, alien' by Andrew Scott, is out of print and hard to get. But your library should have an interlibrary loan service that can get you a copy. Its an easy and fascination read if this topic really interests you.
Thank you NT for the info, but what is ABE? I'd love to get a copy of this book, which to me is an excellant example of how such a book should be written, for my library. I notice that Annafan had no interest in taking me up on my offer of titles of well researched and written literature that responds to his/her question. It is so much more fun to argue from ignorance that to do the hard work of studying what has been learned to date. I know, since that is my own modus operandi. Thanks again, and let me know what ABE is or their URL so I can check them out.