The image resolution of CT angiography currently precludes vessel segmentation of coronary arteries smaller than approximately 1 mm in size and affects blood flow analysis. We propose an algorithm for the generation of patient-specific vascular networks starting from segmented epicardial vessels. We extend a tree generation method based on functional principles to account for multiple, competing vascular trees. From segmented vascular tree models of several patients, we generate networks (~50 vascular trees) filling the entire left ventricle myocardium down to the arteriole size level. All vascular models match morphometry properties previously described and enable potential applications for blood flow simulation and disease modeling.