Eligibility Criteria:
Inclusion Criteria:
* Diagnosis of 1 of the following:
NOTE: Histologic confirmation not required for intrinsic brain stem cell tumor, optic pathway gliomas, pineal tumors and elevations of cerebrospinal fluid, and serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin.
* Histologically confirmed relapsed or refractory solid tumors at original diagnosis including CNS tumors\* (Part 1 and Part 2a)
* Neurologic deficits in patients with CNS tumors must have been relatively stable for ≥ 1 week
* Histologically confirmed soft tissue sarcoma, desmoplastic small round cell tumor, or extraosseus Ewing sarcoma at original diagnosis including the following (Part 2b):
* Tumor in the head, neck, or extremity or fixed within the abdomen or pelvis that it is not sensitive to motion artifact
* No isolated pulmonary metastases
* Disease with no known curative therapy or no therapy proven to prolong survival with acceptable quality of life
* Measurable or evaluable disease (Part 1 and Part 2a)
* Measurable tumor that is ≥ 2 cm in its longest diameter (Part 2b)
* Patients must be:
* \> 2 years of age and ≤ 21 years of age (Part 1 and Part 2a)
* \> 2 years of age and ≤ 25 years of age (Part 2b)
* Body surface area ≥ 0.48 m\^2 (Part 1 and Part 2b)
* For patients with CNS tumors or CNS metastasis, there must be no evidence of new CNS hemorrhage of more than punctate size and/or \> 3 foci of punctate hemorrhage on baseline MRI for primary CNS tumors ≥ 14 days prior to study entry
* Karnofsky performance status (PS) 50-100% (\> 16 years of age)
* Lansky PS 50-100% (≤ 16 years of age)
* Platelet count ≥ 100,000/mm\^3 (transfusion independent)
* ANC ≥ 1,000/mm\^3
* Hemoglobin ≥ 8.0 g/dL (may receive RBC transfusions)
* Creatinine clearance or radioisotope GFR ≥ 70 mL/min OR serum creatinine based on age/gender as follows:
* 0.6 mg/dL (1 to \< 2 years of age)
* 0.8 mg/dL (2 to \< 6 years of age)
* 1 mg/dL (6 to \< 10 years of age)
* 1.2 mg/dL (10 to \< 13 years of age)
* 1.5 mg/dL (male ) or 1.4 mg/dL (female) (13 to \< 16 years of age)
* 1.7 mg/dL (male) or 1.4 mg/dL (female) ( ≥ 16 years of age)
* Urine protein:creatinine ratio \< 1 OR urinalysis negative for protein OR 24-hour urine protein level \< 1 g
* Bilirubin ≤ 1.5 times upper limit of normal (ULN)
* ALT ≤ 110 U/L
* PT and PTT ≤ 1.2 times ULN
* INR ≤ 1.2
* Serum albumin ≥ 2 g/dL
* No grade \> 1 abnormalities of potassium, calcium, magnesium, or phosphorous
* Supplementation allowed
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* Oral contraceptives are not considered effective
* Adequate cardiac function defined as any of the following:
* Shortening fraction of ≥ 27% by echocardiogram
* Ejection fraction of ≥ 50% by gated radionuclide study
* QTc \< 450 msec
* No history of myocardial infarction, severe or unstable angina, or peripheral vascular disease or familial QTc prolongation
* Adequate blood pressure defined as ≤ 95th percentile for age, height, and gender
* Known history of well-controlled seizures allowed
* Able to swallow whole tablets (Part 1 and Part 2b)
* No uncontrolled infection
* No evidence of active bleeding, intratumoral hemorrhage, or bleeding diathesis
* None of the following conditions within the past 6 months:
* Arterial thromboembolic events, including transient ischemic attack or cerebrovascular accident
* Pulmonary embolism
* Deep vein thrombosis
* Other venous thromboembolic event
* No hemoptysis within the past 6 weeks
* No serious or non-healing wound, ulcer, or bone fracture
* No significant traumatic injury within the past 28 days
* No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days
* No patients who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study
* No fine-needle aspiration within 48 hours before day 1 of therapy
* Fully recovered from all prior therapy (e.g., chemotherapy, immunotherapy, or radiotherapy)
* At least 3 weeks since prior myelosuppressive chemotherapy (6 weeks for prior nitrosourea)
* At least 7 days since prior hematopoietic growth factor
* At least 21 days since prior VEGF-Trap
* No prior pazopanib hydrochloride
* At least 7 days since prior VEGF-blocking tyrosine kinase inhibitor or other biological agents
* At least 3 half-lives since prior monoclonal antibody, including bevacizumab
* At least 21 days since any other prior anticancer antibody therapy
* At least 2 weeks since prior local palliative radiotherapy (small port)
* At least 3 months since prior total-body irradiation, craniospinal radiotherapy, or ≥ 50% radiotherapy to the pelvis
* At least 6 weeks since prior other substantial bone marrow radiotherapy
* At least 2 months since stem cell transplantation and no evidence of graft-vs-host disease
* Thyroid replacement therapy allowed provided a stable dose has been received for ≥ 4 weeks
* No concurrent medication for cardiac function or hypertension
* Concurrent corticosteroids allowed provided dose is stable or decreasing for \> 7 days (for patients enrolled in Part 1 and Part 2a of study)
* No concurrent corticosteroids for patients enrolled in Part 2b of the study
* No other concurrent anticancer agents or radiotherapy
* No other concurrent investigational drugs
* No concurrent enzyme-inducing anticonvulsants
* No concurrent anticoagulation therapy with coumadin and/or low molecular weight heparin
* Prophylactic anticoagulation therapy (i.e., intraluminal heparin) of venous or arterial access devices allowed
* No concurrent aspirin, ibuprofen, or other NSAIDs
* No concurrent drugs metabolized through several of the specific P450 cytochrome isoform including inducers or inhibitors of CYP3A4
* No concurrent drugs with a known risk of torsades de pointes
* At least 28 days since prior major surgical procedure, laparoscopic procedure, or open biopsy
* Port placement or central line placement 48 hours before day 1 of therapy allowed
* No core biopsy within the past 7 days