<p>We identify what has been referred to as ‘cut-off CFT’ in holographic braneworld with <i>T</i>² or <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> theory (depending on the dimension of the bulk), so that the holographic dual of AdS-gravity with Neumann boundary conditions is a <i>T</i>²-deformed CFT that is set free. After making statements that apply for general dimensions higher than three, we focus on the case of a three-dimensional bulk. We find from bulk arguments that the effective theory on the brane is governed by a <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation>-like flow equation, such that under certain assumptions the effective gravity theory on the brane is given by a <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation>-like deformed timelike Liouville theory, which limits to the description of the holographic Weyl anomaly for branes that approach the asymptotic boundary.</p>