These paragraphs clarify the extent to which the Scottish Parliament can legislate with regard to a Scottish public authority with mixed functions and a Scottish public authority with no reserved functions.  There are other provisions in the Act which refer to such authorities - see sections 91, 92, 118, 119, Schedule 5, Part II, Sections B13 and L2.
Paragraph 1(1) provides that the Schedule does not reserve any Scottish public authority if some of its functions relate to reserved matters and some do not, unless it is a cross-border public authority.  This is referred to as a Scottish public authority with mixed functions. A Scottish local authority is an example of such an authority.
The expression “Scottish public authority” is defined in section 126(1) as meaning any public body (except the Scottish Parliamentary Corporate Body), public office or holder of such an office whose functions are exercisable in or as regards Scotland. Section 126(3) makes provision for determining whether any function of a public body etc relates to reserved matters.  A cross-border public authority is defined in section 88.
Paragraphs 1(2)  and (3) make it clear that paragraph 1(1) means that the Scottish Parliament can legislate as regards the constitution of the authority (including its establishment and dissolution, its assets and liabilities and its funding and receipts) and as regards conferring or removing any function specifically exercisable in relation to the authority, but not where that function is specifically exercisable in relation to a particular function of the authority if that particular function relates to reserved matters.
Paragraph 2 provides that paragraph 1 of Part I of the Schedule (which reserves aspects of the Constitution) does not reserve any Scottish public authority with functions none of which relate to reserved matters.  This ensures that such authorities are not caught by the reservation of the Crown.  This type of authority is referred to as a Scottish public authority with no reserved functions.
TABLE OF RESERVED MATTERS Detail of Provisions Paragraphs 1 and 2: Scottish public authorities