Each US University will have what’s known as the Common Data Set - essentially detailing admission statistics. If you do a little bit of digging, you can find this for each school (I’d be happy to find one for you, if you give me a particular school to look at).

Anyway, with this data you can see the number of students admitted as transfers. Most top schools accept very few transfer students. For example, here’s Harvard’s common data set for 2014-2015.

Out of 1432 transfer applicants, 13 were admitted and 12 actually enrolled. That’s a 0.8% admission rate for transfers.

For Stanford, in the same time period:

http://ucomm.stanford.edu/cds/2014

Out of 1764 transfer applicants, 33 were admitted and 29 enrolled. That’s a 1.9% admission rate, so slightly better odds than Harvard, but far from great.

Here’s another great resource (although a bit out of date):

http://transferweb.com/stats/transfer-acceptance-rates/#.WHSTZbFh2_M

Some great places like Notre Dame have a 36.94% transfer acceptance rate according to this.

My advice would be to work out what schools you want to target, and have a look for their common data set to work out your odds

Your chances mostly depend on what you do during your first year/2 years in NZ/AU uni. The fact is, it’s very difficult to successfully transfer to the top ten schools in the U.S., because hardly anyone drops out of those schools, so they don’t have much room to take new students in after freshman matriculation. BUT it’s absolutely possible – I transferred to Harvard from a liberal arts university and beat the .8% admissions rate Harry was talking about. Around 1400 applied my year, and 12 got in. The fact is, half of the reason I got in was because the class just didn’t have another student like me – with my same diversity of interests and pursuits – and so admissions knew I would make a contribution to the class, fill a hole.
The GREAT thing about trying to transfer from an NZ/AU uni is that you already stand out, just by virtue of how unusual it is to try to do that. Beyond standing out generally, what it comes down to is this: wherever you’re applying to transfer wants to see that you have completely used up the resources available at your current school. If you’re an average student who doesn’t do much extra-curricularly at your current uni, why on earth would a top school think you need to transfer? They want to perceive that transferring is actually necessary in order for you to reach your full potential, so you have to crush your freshman year wherever you are. That might mean grabbing a leadership position in an established organization or creating a new one; that mean being a team player in a bunch of organizations but excelling in your studies and pursuing passions outside of school. Starting a business, getting published in a magazine or newspaper, volunteering, conducting research with a professor…these are the sorts of go-getter things colleges want to see. I didn’t even have a 4.0 when I transferred to Harvard. If you must know, I wasn’t even that close to having a 4.0. But what I did have was evidence that I had accessed every facet of my current school’s campus, and still wasn’t satisfied. I talked about desiring a community that matched my passion for learning, a community that made me outwardly curious. And I also had the ‘unexpected’ essay, the essay that stuck out from everything else in my application. They asked me what my favorite book was, and I wrote about Winnie the Pooh by A.A. Milne, because, truthfully, it was the book that most stuck out in my mind as defining me and my character over time.
All this is to say: YES, it is possible, but it is not easy. This is why I help people do it through Crimson – embarking on the transfer journey by yourself is never a good idea. When I was applying, I was in touch with multiple people who had transferred in previous years, and I even became close enough with one that he wrote me a letter of recommendation. That’s the power of relationship-building; that’s the power of Crimson.