History of a deep venous thrombosis or a thromboembolism Patients must have an HCC diagnosis (initial, recurrent, progressive and/or refractory to other therapies) by at least one criterion listed below =< 360 days prior to study entry* Pathologically (histologically or cytologically) proven diagnosis of HCC* At least one solid liver lesion or vascular tumor thrombosis (involving portal vein, inferior vena cava [IVC] and/or hepatic vein) > 1 cm with arterial enhancement and delayed washout on multi-phasic computerized tomography (CT) or magnetic resonance imaging (MRI) in the setting of cirrhosis or chronic hepatitis B or C without cirrhosis* For patients whose CURRENT disease is vascular only: enhancing vascular thrombosis (involving portal vein, IVC and/or hepatic vein) demonstrating early arterial enhancement and delayed washout on multi-phasic CT or MRI, in a patient with known HCC (diagnosed previously < 720 days) Patients must not have a prior history of deep vein thrombosis (DVT) or pulmonary embolism in the past 5 years Patients with a history of deep vein thrombosis must be on anti-coagulation therapy prior to enrollment; patients requiring prophylactic anti-coagulation are eligible Significant vascular disease (e.g. aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to day 1 History of deep venous thrombosis or migratory thrombophlebitis (Trousseau) Patients with symptomatic peripheral vascular disease are not eligible Clinically significant peripheral vascular disease or vascular disease (including aortic aneurysm or aortic dissection) Clinical significant peripheral vascular disease or vascular disease (aortic aneurysm or aortic dissection) Clinically significant peripheral vascular disease or abdominal aortic aneurysm (> 5 cm) or aortic dissection; if known history of abdominal aortic aneurysm with >= 4 cm in diameter, all of the following must be met: * An ultrasound (US) within the last 6 months prior to registration will be required to document that it is =< 5 cm* Patient must be asymptomatic from the aneurysm* Blood pressure must be well controlled as defined in this protocol No history of arterial thrombotic events within the past 6 months, including:* Transient ischemic attack (TIA)* Cerebrovascular accident (CVA)* Peripheral arterial thrombus* Unstable angina or angina requiring surgical or medial intervention* Myocardial infarction (MI)* Significant peripheral artery disease (i.e., claudication on less than one block)* Significant vascular disease (i.e., aortic aneurysm, history of aortic dissection) Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before registration Significant cardiovascular or cerebrovascular disease including:* Uncontrolled hypertension (systolic blood pressure [SBP] >= 150; diastolic blood pressure [DBP] >= 90)* History of myocardial infarction within 6 months* Unstable angina* New York Heart Association functional classification II, III or IV* Baseline ejection fraction =< 50% as assessed by echocardiogram or multi-gated acquisition (MUGA)* Cerebral vascular accident (CVA) or transient ischemic attack (TIA) within 6 months* Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or peripheral arterial thrombosis) within 6 months Clinically significant peripheral vascular disease or known abdominal aortic aneurysm ( > 5 cm in diameter) or history of aortic dissection; patients with known history of abdominal aortic aneurysm (AAA) with >= 4 cm in diameter, a repeat ultrasound (US) within the last 6 months prior to randomization will be required to document that it is =< 5 cm, and patient must be asymptomatic from the aneurysm, and the blood pressure must be well controlled as required in this protocol Patients with current deep vein thrombosis or deep vein thrombosis within the past 6 months are not eligible Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to day 1 Patients with clinically significant cardiovascular disease are excluded* Inadequately controlled hypertension (HTN) (systolic blood pressure [SBP] >= 160 mmHg and/or diastolic blood pressure [DBP] >= 90 mmHg despite antihypertensive medication)* History of cerebrovascular accident (CVA) within 6 months* Myocardial infarction or unstable angina within 6 months* New York Heart Association class II or greater congestive heart failure * Serious and inadequately controlled cardiac arrhythmia* Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection)* Clinically significant peripheral vascular disease Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to day 1 Patients with clinically significant cardiovascular disease are excluded* Inadequately controlled hypertension (HTN) (systolic blood pressure [SBP] > 160 mmHg and/or diastolic blood pressure [DBP] > 90 mmHg despite antihypertensive medication)* History of cerebrovascular accident (CVA) within 6 months (see additional requirement for adjuvant protocols)* Myocardial infarction or unstable angina within 6 months (see additional requirement for adjuvant protocols)* New York Heart Association grade II or greater congestive heart failure * Serious and inadequately controlled cardiac arrhythmia* Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection)* Clinically significant peripheral vascular disease Participants with any of the following:* History of myocardial infarction within six months* Unstable angina* History of cerebrovascular accident (CVA) within 6 months* New York Heart Association grade II or greater congestive heart failure* Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection)* Clinically significant peripheral vascular disease