Q:

My Documents view accross site collections, and be able to filter which ones are checkout

We have 16 000 site collections, some users collaborate in many site collections with documents. 
We want to have a view or webpart on the root site collection, that shows all the documents uploaded or created for an specific user. 
How can I achieve that? 
2nd.   Let's suppose for a specific user the view or webpart will return 200 documents, but the user does not remember in which documents he was working on (checked out files). 
It would be great if whatever I develop can filter out based on whether it's checked out or not. 
Any tips? 

A:

Your first option could be achieved using search.   I have done similar in SP2010 and used jQuery to pass the current user to the search web service. 
The second option is more complex as search will ignore any files which have never been checked in.   There are some third party tools such as Lightning Conductor which can scan for files which have not been checked in across multiple site collections but I suspect with the number you have this will be rather slow. 
Again, I have done this in 2010 using a PowerShell script which runs overnight and populates a list with all the checked out files, where they are and who has them checked out.   This means I can then have a little web part which queries the list to present the information to users.   Of course, it has to be accepted that this is not real time but it does achieve the aim.