Most people backed the Assembly retaining the powers it has in six key areas: tourism, agriculture, housing, roads, education and health. But a significant minority want to see responsibility for health and education returned to London.
20% said education should be the responsibility of the UK Parliament and Government and 27% said the NHS should be administered from London. The survey points out that these are two areas which received most media coverage.
More top news
A charity are planning to buy and protect Wales' Celtic 'rainforest'
People experiencing debt related problems in Wales has increased by nearly a fifth in the last year, according to Citizens Advice.
Patients are being urged to seek medical advice as soon as they experience pancreatic cancer symptoms.