User Profile Sync across a One-Way Trust – This one in English

User to run profile sync from trusted/remote domain: add to local admin group.
AD Users & Computers: find computerobject – allow to authenticate above user.

Config People Picker across one-way trust for CA, so you can add it as Farm Administrator:
stsadm -o setapppassword -password WHATEVER
stsadm -o setproperty -url http://URL for CA -pn peoplepicker-searchadforests -pv “forest:BLA.DK.LOCAL; forest:REMOTE.FOREST.DK,domain\username,password
Add remote profile user to Farm Admins group
Run SharePoint Powershell Add-SpShellAdmin <above user>

Log in locally to server as remote profile user
Run SharePoint Powershell $credentials = Get-Credential – Fill in the login box
New-SPManagedAccount –Credential $credentials

Provision User Profile Sync According to Spence Harbars brilliant guide – Set up Service App to run using the remote profile user managed account you just created.

Start FIM SSM (C:\Program Files\Microsoft Office Servers\14.0\Synchronization Service\UIShell\miisclient.exe)
Go to Management Agents screen, right click [SYNCHRONIZATION CONNECTION NAME] and select Properties
Go to Configure Directory Partitions and uncheck the directory partition beginning with CN= – NOTE ITS POSITION ON THE LIST, I.E is it first, second etc – YOU NEED THIS LATER!
Click OK to close Properties window
Again, right click on [SYNCHRONIZATION CONNECTION NAME] and select Configure Run Properties…
On DS_FULLSYNC, DS_DELTASYNC, DS_FULLIMPORT, DS_DELTAIMPORT, delete step for the directory partition you unchecked. NOTE! You must only remove the step for the directory partition you removed earlier on bullet 3. I.e., if the removed directory partition was 3rd on the list, you should delete 3rd Step.
Click OK
Re-run profile synchronization from Central Admin