Plastic syringes for painting come in a large variety of sizes from 1 ml on up to the larger irrigation syringes that can hold up to 100 ml. For painting purposes, syringes without needles are preferred.
When using heavy body paints, a syringe can extrude the paint into a string like form that will hold its shape. This can be dried on a support to give a dimensional quality. The paints that work for this are oils and heavy bodied acrylics. Thinner bodied acrylics can be mixed with a gel medium to increase thickness.
You can see first hand the possibilities of dimensional art at the page where the photo comes from Drexel art.
Jackson Pollock was an abstract expressionist American artist from the middle of the 20th century. Instead of using an easel, Pollock layed his canvas on the floor so he may walk around the painting to be more involved in the creation. Although he used brushes at times, he used them to allow paint to merely drip off them. He also was known to use syringes and even turkey basters to apply his paint.