I can just say that poster baktrak is right. It would be theoretically possible to reach Split from Pula by train, but it would require at least three train changes and too many spent hours on travel. When we talk about the train traveling around Croatia, then it is important to know that the trains are good (in terms of price) when we talk about the connections between the towns on the coast like Split, Šibenik, Zadar and Rijeka with Zagreb (in the continental part) and they are pretty good for travel within the continental part of the country. Unfortunately, the coastal towns are not interconnected by rail network.
So, by far the best option is the one that baktrak has mentioned. Take a catamaran from Pula to Zadar which departs in the morning hours and arrives in Zadar at around noon. Here is the last year's timetable: http://www.miatours.hr/plred07-e.html . Here I have to inform you that the timetable for this season will be published the next week, so please, just remind us to check it for you.
After you have arrived in Zadar, just proceed to the bus station. The only problem here is the fact that the seaport and the bus station are not so close to each other. There are roughly 2 km distance from each other.
From Zadar there are fairly frequent direct bus connections to Split, but the best connections are those that use the old, coastal road. It is really rewarding and scenic and just 30 - 45 minutes slower compared to the lines using the motorway.
Now, you can spend a night in Split (it is fairly attractive and a town that has a lot to offer to its visitor) or to proceed to Hvar by catamaran. Otherwise, you can take a catamaran that departs from Split at 17:00 and arrives in Hvar at 18:15. Here is their timetable: http://www.krilo.hr/en/sailing_schedule.html .
I have to mention that on the route from Split to Hvar, the above mentioned sailing company is not the only one. Beside this one, there is also another catamaran departing from Split at 11:30. Here is the schedule: http://www.jadrolinija.hr/pdfs/9603A.ljeto.2013.e.pdf .
Now, knowing this facts, you can combine what would be the best option for you.
As far as the return from Hvar to Zadar airport is concerned, it is pretty easy to accomplish within a day. Just like this:
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take a catamaran from Hvar to Split at 07:45 with arrival in Split at 08:40
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from Split take the first available bus to Zadar
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from Zadar take a public bus to the airport; here is the timetable for the public bus transfers: http://www.zadar-airport.hr/en/how-to-reach-us ; please, note that this is the timetable valid until May 31, but to be better informed, just visit this site after the mentioned date to be updated
