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.
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Wales have qualified for the Euro 2016 quarter finals after beating Northern Ireland 1-0 in Paris.
A rally has been held in Cardiff following the EU referendum to show support to migrant communities.
It's 0-0 at half time in Paris as Wales face Northern Ireland in the last 16 of Euro 2016.