CalDAV and CardDAV are protocols to synchronize calendars and contacts with a remote server. At the moment, there is no carddav implementation directly accessible from the Ubuntu Touch graphical user-interface, so the only way to sync carddav is by using syncevolution + cron. The basic building blocks can be traced to here, here, here and here, but it took a little bit more before my phone was fully synced to iCloud.

Identify your user ID:

curl -s -X PROPFIND -u "$ICLOUD_LOGIN" -H "Depth: 0"  --data "<propfind xmlns='DAV:'><prop><current-user-principal/></prop></propfind>"  https://caldav.icloud.com/

After providing your app-specific password, you should get something like https://caldav.icloud.com/xxxNNNNNNNxxxxx/principal/

To reference the cluster where the actual calendars is stored:

curl -s -X PROPFIND -u "$ICLOUD_LOGIN" -H "Depth: 0"  --data "<propfind xmlns='DAV:' xmlns:cd='urn:ietf:params:xml:ns:caldav'><prop><cd:calendar-home-set/></prop></propfind>" 
 https://caldav.icloud.com/xxxNNNNNNNxxxxx/principal/

Which should kick back something like https://pNN-caldav.icloud.com:443/xxxNNNNNNNxxxxx/calendars

You can list all the calendars from your iCoud account:

curl -s -X PROPFIND -u "$ICLOUD_LOGIN" -H "Depth: 1"  --data "<propfind xmlns='DAV:'><prop><displayname/></prop></propfind>"  https://pNN-caldav.icloud.com:443/xxxNNNNNNNxxxxx/calendars/

The CardDAV home contains the CardDAV collections (aka the 'address books'), not the vCards (which contain contacts and contact groups). If you redirect the previous steps to https://contacts.icloud.com, and follow the same sequence, you need to take one more hop.

This is how you eventually arrive at

iCloud_CalDAV_URL="https://pNN-caldav.icloud.com:443/xxxNNNNNNNxxxxx/calendars/home/"

iCloud_CardDAV_URL="https://pNN-contacts.icloud.com:443/xxxNNNNNNNxxxxx/carddavhome/card/"