Ok, thanks. This is helpful. But I am still wondering if it wouldn't be better if the client only uses the .com domain and target with this domain also in the UK.
In this way you only have to build authority on the .com domain instead of on two domains?

Or does Google sent the authority build on the .com domain trough to the .co.uk domain with these codes?

Cheers!

Gerjan

Hello,

A new client of mine has an .com and an .co.uk domain. Both the same content (and they don't have the capacity to make specific content on both domains).

I am thinking building al domain authority to 1 domain. In this case the .com domain. 
And forward the .co.uk to this .com domain.
In this way, the .com will rank in both UK as in other English speaking countries, right? Or not?
Or should I use the  rel="alternate" hreflang="x" tag?

I am not sure. But I do know big brands rank high in the Netherlands with .com domains (for example booking.com).

Looking forward on feedback on best practices here...

Thanks!