Eliminating Thermal Isolation Pads in Eagle
The common name is "thermal relief".  

No, it doesn't limit the current. For changes in current the resistance must be at least, say, 1 % of the other resistance. My rule-of-thumb: a 1 mm trace of 35 &micro;, 1 m long has a resistance of 0.5 &Omega;. The length of the spokes is determined by the backoff. My design rules have a standard 0.2 mm for that, and I use a 0.35 mm width. Then the resistance of one spoke is 0.5 &Omega; x 0.2 (mm/mm) x 0.35 (mm/m) = 35 &micro;&Omega;. Then 4 spokes are 9 &micro;&Omega;. 

You can immediately see that this is negligible. a 5 A current will cause a 44 &micro;V drop, and a 55 &micro;W dissipation per spoke.