Dear Everybody
One other project I would like to start involves pumps.
I wanted to have the thinnest pump possible (e.g. Thumb sized) and the equivalent small tubes. This would be controlled by the arduino and after certain time unit with pressure spray out water.
If possible run with a battery.
I couldnt find a lot on this online.
Only really big clumsy pumps.
Since the tubes are so small, they will not need a lot of power I hope and can be run by a battery.
Thanks!
You could try making your own, looking around I saw an instructible, and there was a youtube video, not as small as you'd like but pretty small...
There are more YT videos available... of course if you can think of something that uses a tiny pump then you can just buy one of those... I tried aquariums, apparently they have big pumps 
never had a fish in my life
So skip the pump, and just a have an elevated tank supplying header pressure to a valve that you control instead.
Google drink bot, or " arduino breast milk pump".
Sorry I can not post links yet.. 
Small aquarium pumps? They are normally powered by 120vac, so either SSR or simple relays would be required.
Lefty
This is probably the smallest pump you'll be able to find - its an inline reciprocating pump powered by 16 VAC, 2.75" long x 1" diameter, and pretty powerful for its size:
I'm not sure if you can get these anywhere else besides Edmund's; their stuff always tends to "feel" overpriced - and this pump is no exception.
Something you have to keep in mind when it comes to water pumps is "small size" and "high pressure" tend to be inversely proportional - you should see the size of the pumps needed for the Fountain Hills, Arizona fountain:
...at one time, it was the highest shooting fountain in the world (now fourth highest). When that sucker's running, the ground vibrates.
Here's a 12VDC marine fresh water pump (larger than the Edmund's, but cheaper - and DC):
http://www.defender.com/product.jsp?path=-1|51|299222|121271|826345&id=961700
You might try contacting this company of miniature pumps:
Don't expect them to be cheap, though.
One other possibility (though probably not as small as you want) would be a windshield wiper washer pump; they run off 12 VDC, and are very powerful for their size (the motors are pretty high current). You could probably find some serviceable ones at an auto salvage yard (or other auto parts places).