The invention provides an integrated ablation system using a catheter with multiple irrigation lumens. The catheter adapted for ablation has multiple dedicated irrigation tubings to supply fluid to their respective electrode or set of electrodes. The tubings provide parallel flow pathways through the catheter where irrigation fluid is delivered to irrigate tip and/or ring electrodes which can accomplish uni-polar or bi-polar ablation. Such separate and dedicated fluid pathways allow fluid to be delivered to the corresponding electrode or set of electrodes at different flow rates. An integrated ablation system using such catheter has an ablation energy source and an irrigation pump with multiple pump heads that can operate independently of each other. An integrated irrigation tubing set is included to extend between the fluid source and the catheter, with each pump head being able to act on a different tubing that delivers fluid to a different electrode or set of electrodes.