Most of the EU majors have a cadet scheme which takes ab-initio students from their first flight to the right seat of an airliner at no charge to the student; this we call 'sponsorship' in UK (or we did, when it existed!). Many other airlines run schemes where the cost of training is shared between the carrier and the cadet - this would be 'part-sponsorship'. The numbers of pilots derived from these schemes is quite small in the overall market.
Military aviation in the EU is nowhere near as large as it is in the US (and has been contracting for many years), and a greater proportion of EU military pilots remain with the military for their entire career rather than leave for civilian aviation, therefore the military are now less important as a source of pilots - though still significant, and highly valued.
At the moment, the largest source of commercial pilots in the UK, and probably the rest of the EU, are those who have paid for their own training and are working their way up via night freight, para dropping etc to an airline cockpit - though some will succeed in getting employed in a 737/A320 directly from their CPL course.
I hope this goes some way to answering your question.
Scroggs