I will argue that the 10 domains will be seen as, at least, low quality domains with low trust scores and will likely never rank with 10 articles each assuming that they are a blog. There is an exception for business sites which would be seen by the search engine a bit differently. Here is why.
Blogs are highly competitive. With so many blogs with many articles that are designed specifically to penetrate the SERPs for specific and planned search queries, just a few posts will likely get lost in the sea of work.
A business site is another matter as @SimonHayter rightly points out. Thank You Simon! If these are individual businesses, then that is a whole other matter. In the case of individual businesses, what becomes important is the NAP (name, address, phone number) of the business. I highly recommend exploring using schema.org mark-up for this. I have found the best place to put this information is in the sites page template footer so that it appear on each page.
What makes a business rank is much smaller criteria for business searches which include services and locale. For article search however, there are a lot of factors including the volume of competition. If you are talking about a totally new or untouched topic, then the competition will be light, however, generally, this is not the case.
But please do keep in mind what I say about SERP penetration and and duplicate content in the next few paragraphs.
Google makes every effort to cluster sites into relationships using a semantics based database. It will be relatively simple for Google to determine that these domains are related by ownership using several factors. Keep in mind that Google, being a registrar, will be able to see the registration information even when made private. As well, it is relatively easy to determine if a series of websites are on a single server or instance when hosting. There are quire a few other factors Google can use to cluster sites so please keep this in mind.
Google will also use semantics (linguistics) to determine the topic of these sites. Google will see that these sites are related by topic. Please know that posts do not have to be linear duplicates to determine them to be duplicates. In semantics, each post will be scored using several standard algorithms and combinations of algorithms and placed into a matrix. It is a simple matter of comparing scores found within these matrices to determine that the posts are at least similar enough to be duplications.
Keep in mind that these kinds of analysis have been in place since 2003, 2005, and 2008. This form of analysis is highly effective.
Each site will not be able to rank with just 10 articles assuming it is a blog site. Even a business site cannot expect much if any traction from just a few articles. It is just not enough to penetrate into the SERPs. As well, none of the sites will become authoritative on any topic. Authority is a powerful signal.
Having several domains with the same topic and minimal posts each, Google will likely see this as an attempt to game the SERPs unless the sites are business sites which will rank for other reasons.
I argue that it is always far better to have one domain that ranks well. If, for example, you put your efforts into a single domain, you can potentially have 100 posts which would penetrate the SERPs better. There is no quick way to gain a solid presence in the SERPs and gain traction. It just plain takes time and effort. There are no shortcuts, tricks, loop-holes, or technique that will speed this process up except for real work, time, and dedication. It is far better to put your work into one domain and make a name for yourself as an authority.