Are you hoping to publish in a peer-reviewed journal? If so, I expect your dissertation will need to go through substantial revisions. More specifically, I expect your dissertation will need to be condensed to some extent. Many journals for example want articles less than 5000 words, and I expect your dissertation, even in three papers, would be larger than this.
It is possible that your dissertation is brief and will require minimal changes, but this is not often the case. I would check what journals you want to submit to, and check their length requirements. Often manuscripts based off of manuscripts feel like they were originally a manuscript, and not in a good way. Journal articles often get to the point quite quicker. For example, in original research articles (not reviews and such), introductions vary from 500-3000 words depending on the field (more is possible, of course). In a dissertation, an introduction might be 30 pages!
Your dissertation likely also covers a fair bit of breadth. Make sure to include in a manuscript only the information that is relevant to that specific paper and line of thinking.
I'm assuming this question is about the content/format, and not copyright and such. If you are wondering about copyright, my impression is what in most cases you can submit your dissertation exactly as it is for publication, unless you have already signed your copyright away.