will not capture important (and sometimes poorly understood) effects, among them planetary migration (e.g., @kn_2012; @dhm_2014; @dk_2015 [@dk_2017]; @fc_2017; @kts_2018; @mnp_2020), eccentricity evolution (both of the planet and the disc; e.g., @pnm_2001; @gs_2003; @kd_2006; @dc_2015; @mfv_2019), and the 3D dynamics of circumplanetary discs (e.g., @fzc_2019). Our goal is not so much to be realistic but to acquire some intuition about the interplay of Lindblad repulsion and planetary accretion, and to provide a baseline understanding that can guide the development and interpretation of more sophisticated models. Where possible, we place our results in context with state-of-the-art numerical experiments in the literature (see in particular section \[sec:sum\]).

Viscous discs: Surface Density Profiles at Fixed Planet Mass {#sec:consumption}
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We study how the surface densities of viscous accretion discs are shaped by repulsive planetary Lindblad torques in addition to planetary accretion of disc gas (“consumption”). Section \[sec:oom\] contains analytic considerations which are tested numerically in section \[sec:num\]. In these sections, while we allow the disc surface density to deplete by consumption, we do not simultaneously allow the planet’s mass to increase. This fixing of the planet’s mass is done for simplicity, to see how the planet affects the disc but not vice versa. 