Hey Daniel
I am not sure there is ever a single right or wrong answer in these situations as there are just so many moving parts.
I tend to lean towards a single site as, well, it's a single site so just one site to maintain and focus on. But, we have to consider the differences in the business areas and if one area is airplanes and the other is icecream then... maybe the differences are just too pronounced.
I think a helpful way to decide is to consider the likely users and audience for the site(s).
- Who is the site for? What do our typical users look like?
- Do people understand that A is the parent company of X, Y & Z
- Is it going to work for users best as one site or three or does it not really matter
- Who is going to maintain the site and add content?
- Are there any business reasons to have separate sites?
From a pure SEO perspective, three sites would likely give you more scope with each site being truly focused on it's core area, but that comes with the burden of much more work.
With a single site everything is simplified and as long as we ensure we have a very sensible structure and a good clean hierarchy then we should be able to make it easy for a user to navigate and understand where they are within the site and for Google to understand the three different and distinct areas.
I am thinking bread crumbs, URLs, consistent page titles etc.
URL: www.example.com/airplanes/
Breadcrumb: Home > Airplanes
Page Title: Airplanes - Example.com
URL: www.example.com/icecream/
Breadcrumb: Home > Icecream
Page Title: Ice Cream - Example.com
URL: www.example.com/underpants/
Breadcrumb: Home > Underpants
Page Title: Underpants - Example.com
It's all too easy to overcomplicate things and certainly three or even four sites is way more complicated than one. Just remember your users, consider how they may arrive at the site and make sure the structure, breadcrumbs, page names, page titles and everything else all create a consistent experience.
Likewise, ensure that the homepage makes it very easy for people to get to where they need to be (think signposts).
Who knows as well, there may be opportunity to cross sell in having the three businesses on one site and certainly additional marketing like email marketing, analytics, PPC etc all creates extra work to manage effectively on several sites compared to a single site.
If this was me I would be gunning for a single site but with a serious consideration of the pros, cons and any problems or opportunities that may make one or three a better choice.
So, not an answer as such, but maybe something to get you thinking along the right lines.
Hope it helps!
Marcus